How would different Protestant denominations reconcile Matthew 5:19 with the notion of being saved by grace?

The Reformed tradition would say that we are still required to keep the law, even though we are not saved by our works. God still wants us to do what He has commanded us to do, even though we are never justified on the basis of our works. Our motivation is different than those who are not saved, because rather than doing works as an attempt to save ourselves, instead, we do good works out of gratitude to God and a desire to love and serve Him. As Christ says in John 14:15, "If ye love me, keep my commandments."

Belgic Confession of Faith, Article 24

We believe that this true faith, produced in us by the hearing of God’s Word and by the work of the Holy Spirit, regenerates us and makes us new creatures, causing us to live a new life and freeing us from the slavery of sin. Therefore, far from making people cold toward living in a pious and holy way, this justifying faith, quite to the contrary, so works within them that apart from it they will never do a thing out of love for God but only out of love for themselves and fear of being condemned. So then, it is impossible for this holy faith to be unfruitful in a human being, seeing that we do not speak of an empty faith but of what Scripture calls “faith working through love,” which moves people to do by themselves the works that God has commanded in the Word. These works, proceeding from the good root of faith, are good and acceptable to God, since they are all sanctified by God’s grace. Yet they do not count toward our justification— for by faith in Christ we are justified, even before we do good works. Otherwise they could not be good, any more than the fruit of a tree could be good if the tree is not good in the first place. So then, we do good works, but not for merit— for what would we merit? Rather, we are indebted to God for the good works we do, and not God to us, since God “is at work in [us], enabling [us] both to will and to work for his good pleasure” — thus keeping in mind what is written: “When you have done all that you were ordered to do, say, ‘We are worthless slaves; we have done only what we ought to have done.’“ Yet we do not wish to deny that God rewards good works— but it is by grace that God crowns these gifts. Moreover, although we do good works we do not base our salvation on them; for we cannot do any work that is not defiled by our flesh and also worthy of punishment. And even if we could point to one, memory of a single sin is enough for God to reject that work. So we would always be in doubt, tossed back and forth without any certainty, and our poor consciences would be tormented constantly if they did not rest on the merit of the suffering and death of our Savior.

Heidelberg Catechism, Q&A 86 and 87

Q. Since we have been delivered from our misery by grace through Christ without any merit of our own, why then should we do good works?

A. Because Christ, having redeemed us by his blood, is also restoring us by his Spirit into his image, so that with our whole lives we may show that we are thankful to God for his benefits, so that he may be praised through us, so that we may be assured of our faith by its fruits, and so that by our godly living our neighbors may be won over to Christ.

Q. Can those be saved who do not turn to God from their ungrateful and unrepentant ways?

A. By no means. Scripture tells us that no unchaste person, no idolater, adulterer, thief, no covetous person, no drunkard, slanderer, robber, or the like will inherit the kingdom of God.

Canons of Dort, Article 13

In their awareness and assurance of this election, God’s children daily find greater cause to humble themselves before God, to adore the fathomless depth of God’s mercies, to cleanse themselves, and to give fervent love in return to the One who first so greatly loved them. This is far from saying that this teaching concerning election, and reflection upon it, make God’s children lax in observing his commandments or carnally self-assured. By God’s just judgment this does usually happen to those who casually take for granted the grace of election or engage in idle and brazen talk about it but are unwilling to walk in the ways of the chosen.

Presbyterians hold to this same position:

I. Good works are only such as God has commanded in His holy Word, and not such as, without the warrant thereof, are devised by men, out of blind zeal, or upon any pretence of good intention.

II. These good works, done in obedience to God's commandments, are the fruits and evidences of a true and lively faith: and by them believers manifest their thankfulness, strengthen their assurance, edify their brethren, adorn the profession of the Gospel, stop the mouths of the adversaries, and glorify God, whose workmanship they are, created in Christ Jesus thereunto,[ that, having their fruit unto holiness, they may have the end, eternal life.

III. Their ability to do good works is not at all of themselves, but wholly from the Spirit of Christ. And that they may be enabled thereunto, beside the graces they have already received, there is required an actual influence of the same Holy Spirit, to work in them to will, and to do, of His good pleasure: yet are they not hereupon to grow negligent, as if they were not bound to perform any duty unless upon a special motion of the Spirit; but they ought to be diligent in stirring up the grace of God that is in them.

IV. They who, in their obedience, attain to the greatest height which is possibly in this life, are so far from being able to supererogate, and to do more than God requires, as that they fall short of much which in duty they are bound to do.

V. We cannot by our best works merit pardon of sin, or eternal life at the hand of God, by reason of the great disproportion that is between them and the glory to come; and the infinite distance that is between us and God, whom, by them, we can neither profit, nor satisfy for the debt of our former sins, but when we have done all we can, we have done but our duty, and are unprofitable servants: and because, as they are good, they proceed from His Spirit, and as they are wrought by us, they are defiled, and mixed with so much weakness and imperfection, that they cannot endure the severity of God's judgment.

VI. Notwithstanding, the persons of believers being accepted through Christ, their good works also are accepted in Him; not as though they were in this life wholly unblamable and unreproveable in God's sight; but that He, looking upon them in His Son, is pleased to accept and reward that which is sincere, although accompanied with many weaknesses and imperfections.

VII. Works done by unregenerate men, although for the matter of them they may be things which God commands; and of good use both to themselves and others: yet, because they proceed not from an heart purified by faith; nor are done in a right manner, according to the Word; nor to a right end, the glory of God, they are therefore sinful and cannot please God, or make a man meet to receive grace from God: and yet, their neglect of them is more sinful and displeasing unto God.

• Westminster Confession of Faith, Chapter 16

The Reformed Baptists hold to this same position:

1. Good works are only such as God hath commanded in his Holy Word, and not such as without the warrant thereof are devised by men out of blind zeal, or upon any pretence of good intentions.

2. These good works, done in obedience to God's commandments, are the fruits and evidences of a true and lively faith; and by them believers manifest their thankfulness, strengthen their assurance, edify their brethren, adorn the profession of the gospel, stop the mouths of the adversaries, and glorify God, whose workmanship they are, created in Christ Jesus thereunto, that having their fruit unto holiness they may have the end eternal life.

3. Their ability to do good works is not at all of themselves, but wholly from the Spirit of Christ; and that they may be enabled thereunto, besides the graces they have already received, there is necessary an actual influence of the same Holy Spirit, to work in them to will and to do of his good pleasure; yet they are not hereupon to grow negligent, as if they were not bound to perform any duty, unless upon a special motion of the Spirit, but they ought to be diligent in stirring up the grace of God that is in them.

4. They who in their obedience attain to the greatest height which is possible in this life, are so far from being able to supererogate, and to do more than God requires, as that they fall short of much which in duty they are bound to do.

5. We cannot by our best works merit pardon of sin or eternal life at the hand of God, by reason of the great disproportion that is between them and the glory to come, and the infinite distance that is between us and God, whom by them we can neither profit nor satisfy for the debt of our former sins; but when we have done all we can, we have done but our duty, and are unprofitable servants; and because as they are good they proceed from his Spirit, and as they are wrought by us they are defiled and mixed with so much weakness and imperfection, that they cannot endure the severity of God's punishment.

6. Yet notwithstanding the persons of believers being accepted through Christ, their good works also are accepted in him; not as though they were in this life wholly unblameable and unreprovable in God's sight, but that he, looking upon them in his Son, is pleased to accept and reward that which is sincere, although accompanied with many weaknesses and imperfections.

7. Works done by unregenerate men, although for the matter of them they may be things which God commands, and of good use both to themselves and others; yet because they proceed not from a heart purified by faith, nor are done in a right manner according to the word, nor to a right end, the glory of God, they are therefore sinful, and cannot please God, nor make a man meet to receive grace from God, and yet their neglect of them is more sinful and displeasing to God.

• London Baptist Confession of Faith 1689, Chapter 16

Anglicans hold to this same position:

Although the Law given from God by Moses, as touching Ceremonies and Rites, do not bind Christian men, nor the Civil precepts thereof ought of necessity to be received in any commonwealth; yet notwithstanding, no Christian man whatsoever is free from the obedience of the Commandments which are called Moral.

• 39 Articles, Section 7

and:

Albeit that Good Works, which are the fruits of Faith, and follow after Justification, cannot put away our sins, and endure the severity of God's judgement; yet are they pleasing and acceptable to God in Christ, and do spring out necessarily of a true and lively Faith; insomuch that by them a lively, Faith may be as evidently known as a tree discerned by the fruit.

• 39 Articles, Section 12

General Baptists don't really have a common confession to examine, and also have a variety of viewpoints on the issue.

The United Methodist Church holds to this same position:

We believe good works are the necessary fruits of faith and follow regeneration but they do not have the virtue to remove our sins or to avert divine judgment. We believe good works, pleasing and acceptable to God in Christ, spring from a true and living faith, for through and by them faith is made evident.

• United Methodist Confession of Faith, Article 10

The Lutheran Church holds to this same position:

Also they teach that this faith is bound to bring forth good fruits, and that it is necessary to do good works commanded by God, because of God's will, but that we should not rely on those works to merit justification before God. For remission of sins and justification is apprehended by faith, as also the voice of Christ attests: When ye shall have done all these things, say: We are unprofitable servants. Luke 17:10. The same is also taught by the Fathers. For Ambrose says: It is ordained of God that he who believes in Christ is saved, freely receiving remission of sins, without works, by faith alone.

• Augsburg Confession, Article 6

and also:

Our teachers are falsely accused of forbidding Good Works. For their published writings on the Ten Commandments, and others of like import, bear witness that they have taught to good purpose concerning all estates and duties of life, as to what estates of life and what works in every calling be pleasing to God. Concerning these things preachers heretofore taught but little, and urged only childish and needless works, as particular holy-days, particular fasts, brotherhoods, pilgrimages, services in honor of saints, the use of rosaries, monasticism, and such like. Since our adversaries have been admonished of these things, they are now unlearning them, and do not preach these unprofitable works as heretofore. Besides, they begin to mention faith, of which there was heretofore marvelous silence. They teach that we are justified not by works only, but they conjoin faith and works, and say that we are justified by faith and works. This doctrine is more tolerable than the former one, and can afford more consolation than their old doctrine.

Forasmuch, therefore, as the doctrine concerning faith, which ought to be the chief one in the Church, has lain so long unknown, as all must needs grant that there was the deepest silence in their sermons concerning the righteousness of faith, while only the doctrine of works was treated in the churches, our teachers have instructed the churches concerning faith as follows:—

First, that our works cannot reconcile God or merit forgiveness of sins, grace, and justification, but that we obtain this only by faith when we believe that we are received into favor for Christ's sake, who alone has been set forth the Mediator and Propitiation, 1 Tim. 2:5, in order that the Father may be reconciled through Him. Whoever, therefore, trusts that by works he merits grace, despises the merit and grace of Christ, and seeks a way to God without Christ, by human strength, although Christ has said of Himself: I am the Way, the Truth, and the Life. John 14:6.

This doctrine concerning faith is everywhere treated by Paul, Eph. 2:8: By grace are ye saved through faith; and that not of your selves; it is the gift of God, not of works, etc.

And lest any one should craftily say that a new interpretation of Paul has been devised by us, this entire matter is supported by the testimonies of the Fathers. For Augustine, in many volumes, defends grace and the righteousness of faith, over against the merits of works. And Ambrose, in his De Vocatione Gentium, and elsewhere, teaches to like effect. For in his De Vocatione Gentium he says as follows: Redemption by the blood of Christ would become of little value, neither would the preeminence of man's works be superseded by the mercy of God, if justification, which is wrought through grace, were due to the merits going before, so as to be, not the free gift of a donor, but the reward due to the laborer.

But, although this doctrine is despised by the inexperienced, nevertheless God-fearing and anxious consciences find by experience that it brings the greatest consolation, because consciences cannot be set at rest through any works, but only by faith, when they take the sure ground that for Christ's sake they have a reconciled God. As Paul teaches Rom. 5:1:Being justified by faith, we have peace with God. This whole doctrine is to be referred to that conflict of the terrified conscience, neither can it be understood apart from that conflict. Therefore inexperienced and profane men judge ill concerning this matter, who dream that Christian righteousness is nothing but civil and philosophical righteousness.

Heretofore consciences were plagued with the doctrine of works, they did not hear the consolation from the Gospel. Some persons were driven by conscience into the desert, into monasteries hoping there to merit grace by a monastic life. Some also devised other works whereby to merit grace and make satisfaction for sins. Hence there was very great need to treat of, and renew, this doctrine of faith in Christ, to the end that anxious consciences should not be without consolation but that they might know that grace and forgiveness of sins and justification are apprehended by faith in Christ.

Men are also admonished that here the term "faith" does not signify merely the knowledge of the history, such as is in the ungodly and in the devil, but signifies a faith which believes, not merely the history, but also the effect of the history—namely, this article: the forgiveness of sins, to wit, that we have grace, righteousness, and forgiveness of sins through Christ.

Now he that knows that he has a Father gracious to him through Christ, truly knows God; he knows also that God cares for him, and calls upon God; in a word, he is not without God, as the heathen. For devils and the ungodly are not able to believe this article: the forgiveness of sins. Hence, they hate God as an enemy, call not upon Him, and expect no good from Him. Augustine also admonishes his readers concerning the word "faith," and teaches that the term "faith" is accepted in the Scriptures not for knowledge such as is in the ungodly but for confidence which consoles and encourages the terrified mind.

Furthermore, it is taught on our part that it is necessary to do good works, not that we should trust to merit grace by them, but because it is the will of God. It is only by faith that forgiveness of sins is apprehended, and that, for nothing. And because through faith the Holy Ghost is received, hearts are renewed and endowed with new affections, so as to be able to bring forth good works. For Ambrose says: Faith is the mother of a good will and right doing. For man's powers without the Holy Ghost are full of ungodly affections, and are too weak to do works which are good in God's sight. Besides, they are in the power of the devil who impels men to divers sins, to ungodly opinions, to open crimes. This we may see in the philosophers, who, although they endeavored to live an honest life could not succeed, but were defiled with many open crimes. Such is the feebleness of man when he is without faith and without the Holy Ghost, and governs himself only by human strength.

Hence it may be readily seen that this doctrine is not to be charged with prohibiting good works, but rather the more to be commended, because it shows how we are enabled to do good works. For without faith human nature can in no wise do the works of the First or of the Second Commandment. Without faith it does not call upon God, nor expect anything from God, nor bear the cross, but seeks, and trusts in, man's help. And thus, when there is no faith and trust in God all manner of lusts and human devices rule in the heart. Wherefore Christ said, John 15:5: Without Me ye can do nothing; and the Church sings:

Lacking Thy divine favor,

There is nothing found in man,

Naught in him is harmless.

• Augsburg Confession, Article 20