Do Arminian Protestants agree with Chapter 3 Article 1 of the Westminster Confession of Faith?

As an Arminian-leaning Protestant, I agree with this section of the WCF, going as far as to agree with this quote from R.C. Sproul: "If there is one single molecule in this universe running around loose, totally free of God's sovereignty, then we have no guarantee that a single promise of God will ever be fulfilled."

While I think there could be stronger passages in support of the three points (I quite like Joshua 2:15 and Deutoronomy 30:19 in support of human choice, for example), I don't think the exegesis is problematic.

If the underlying question to your question is how do Arminian Protestants reconcile these two things (God ordaining all things, and man still having freedom), I believe the theological framework that best explains this (which I myself hold) is Molinism (other link). I explain it a little in my answer to this question, but to summarize the idea:

God predestines all people without violating their free will by means of what is called His Middle Knowledge; that is, His knowledge of what any free being would choose to do under any set of circumstances. By bringing about any given set of those circumstances, he also brings about the resulting choice with certainty. The key is that the creature isn't somehow "bound" or determined to make that choice; in other words, they don't have to make any particular choice, but God knows what they will choose.

I have recently read material that gives a comparison between the Westminster Confession of Faith [WCF] on "God's Eternal Decree" and a later credal revision of the United Presbyterian Church of North America, which might serve to demonstrate how subtle changes have taken place with an Arminian Protestant view slipping in. This is particularly in response to your request that an Arminian Protestant view be explained re. the WCF 3.1. "What do they believe about it, do they think it’s biblical or not?"

Well, if they thought the WCF on God's Eternal Decree was entirely biblical, they would not have felt the need to change their 1858 doctrine on this (which was consistent with the Bible), to a statement of belief in 1925 that was then at odds with what they had previously held to be entirely biblical. To demonstrate this one example, I shall need to fully quote the UPC of North America stance of 1858, and then their changed stance from 1925 onward.

Please bear in mind here that Arminianism teaches that God's saving grace is for all alike. The stance is taken that if God gave his Son to die for the redemption of all mankind ruined by the fall, but foresaw that, left to themselves they would reject Christ and be lost, then God would graciously elect recipients to receive the special effectual grace of the Holy Spirit, for their salvation. God brings about the events / circumstances that will result in them making the right choice, God knowing with certainty what they will choose. Now, one can consistently hold that God bestows saving grace alike upon all men and that all men will be saved. One can also consistently hold that God bestows saving grace upon some men only and that they only will be saved. But nobody can consistently maintain that God has universal saving grace which does not universally save. Now spot the example of this, with the two comparisons in shifting doctrine, which shows the Arminian view slipping in after amending their first position:

"We declare, that our Lord Jesus Christ did, by the appointment of the Father, and by his own gracious and voluntary act, place himself in the room of a definite number who were chosen in him before the foundation of the world; so that he was their true and proper legal surety; and as such, did, in their behalf, satisfy the justice of God, and answer all the demands which the law had against them, and thereby infallibly obtain for them eternal redemption." The UPC of North America statement of doctrine in 1858.

"We believe that our Lord Jesus Christ, by the appointment of the Father, and by his own gracious and voluntary act, gave himself a ransom for all; that as a substitute for sinful man his death was a propitiatory sacrifice of infinite value, satisfying Divine justice and holiness, and giving free access to God for pardon and restoration; and that this atonement, though made for the sin of the world, becomes efficacious to those only who are led by the Holy Spirit to believe in Christ as their Saviour." The UPC of North America statement of doctrine in 1925. The Westminster Confession of Faith for Study Classes page 36, G.I. Williamson, Presbyterian and Reformed Publishing Co., 1964

The first statement says that Christ was a substitute for some men; the second, he was a substitute for all men.

The first statement says that he suffered the penalty of some men, the second, he suffered the penalty of all.

The first statement says that by his finished work he obtained eternal redemption for those he represented; the second, that he merely obtained access to God for the obtaining of redemption, and this for all.

The 1858 doctrine taught that some men are saved because the Father, the Son, and the Holy Ghost acted to save them. The 1925 doctrine adds a specific statement indicating that only some are actually saved because the Holy Spirit's work is not in harmony with that of God the Son!

If God the Son dies to save everyone, but the Holy Spirit leads only some, then this is surely implicating God as being divided in the three Persons, with a ransom having been given for all, yet not all being redeemed! Thus Universalism arises out of such changes to what was, in 1858 a statement in agreement with the WCF stance on God's eternal decree. But by 1925 changes were made that proposed a 'better' view of how man's will could be accommodated to a more 'generous' scheme of salvation that has to (logically) lead to the doctrine of Universalism if the Holy Spirit is not to be presented as at odds with the work of Christ. I did say this was subtle.

Edit For Completion: The Arminian view of free will is at odds with the WCF view as in III.1 regarding the will of the creature. Arminianism claims that although man was affected by the Fall, he was not totally incapable of choosing spiritual good. The WCF upholds man’s total inability in that respect. Arminianism seems to think of “freedom” as man having the power to do good (or evil) while the WCF speaks of freedom as “the absence of external coercion”. Internally, the sinful nature controls man, so that all his choices will be sinful. Notice that saying a man is able to do good or evil, is very different from saying that a man is at liberty to do what he desires. The WCF maintains that man has liberty but not ability to do what is right. While free from coercion from the ‘outside’, he is not free from the control of his own sinful nature. Arminianism seems to mix up freedom with free will.

Does this make God the author of sin? Not according to the WCF. Why not? Because God cannot foresee that a thing actually will be until he has determined that it shall be, otherwise he would not be the only self-existent being. Arminianism, on the other hand, maintains that God foresees what he had not determined, because it is up to the free-will choice of the individual to finalise the problem of his sin. (Ibid. pp 31 & 273)

To put it crudely, God takes nine steps, but it is up to the will of the individual to take the 10th step that will complete the ‘transaction’. But the WCF is clear that God chooses to grant spiritual life to a spiritually ‘dead’ person, who only then desires to do good and does good. Because man is not free from the control of his sinful nature (as the WCF states) then God cannot be held accountable for any sinful choices sinners make. Man alone is accountable for his sin. God alone can deliver from sin, and he chooses to do so, his way, for those whom he foreordains, as an act of pure grace, not contingent on any meritorious choice or actions of any humans.

Arminianism holds that God predestines to everlasting life those he foresees will, by their own power, turn to him. Sadly, this inadvertently makes God appear to be the author of sin because he leaves it up to sinners to take or leave an incomplete plan of salvation – completion depending on the choice of sinners, and not on the finished work of Christ on the cross, who died for some, and not for all.

This exemplifies several ways in which Arminian Protestantism does not actually agree with the WCF III.1.