How is ignoring clear Biblical instructions in Leviticus justified?

I believe that this passage from Hebrews 9 gives some clarity in that the old covenant was fufilled by Jesus' life and death and therefore not applicable thereafter. All of Hebrews 8-10 give some really important context in my opinion.

"11 But when Christ came as high priest of the good things that are now already here,[a] he went through the greater and more perfect tabernacle that is not made with human hands, that is to say, is not a part of this creation. 12 He did not enter by means of the blood of goats and calves; but he entered the Most Holy Place once for all by his own blood, thus obtaining[b] eternal redemption. 13 The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. 14 How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death,[c] so that we may serve the living God!

15 For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance—now that he has died as a ransom to set them free from the sins committed under the first covenant."

Hebrews 9:11-15

The Apostles themselves, inspired, we believe, by the Holy Spirit, taught that it was no longer necessary to follow all the requirements spelled out in the Mosaic Law:

Acts 15:19–20,24

19 Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
20 But that we write unto them, that they abstain from pollutions of idols, and from fornication, and from things strangled, and from blood.

24 Forasmuch as we have heard, that certain which went out from us have troubled you with words, subverting your souls, saying, Ye must be circumcised, and keep the law: to whom we gave no such commandment

The dietary restrictions God gave to the nation of Israel included prohibitions against eating pork, shrimp, shellfish and many types of seafood, most insects, scavenger birds, and various other animals. The dietary rules were never intended to apply to anyone other than the Israelites. The purpose of the food laws was to make the Israelites distinct from all other nations. After this purpose had ended, Jesus declared all foods clean (Mark 7:19).

Under the Old Testament Law, not only was eating pork forbidden, but even touching the meat of swine made one ritually unclean (Deuteronomy 14:8). This detail further insulated the Israelites from pagan practices. The Canaanites kept herds of swine and sacrificed them to idols. God wanted His people to distance themselves from all such activity. By following the hundreds of dietary rules and regulations God gave to the Israelites, they would also be protected from disease: “If you pay attention to his commands and keep all his decrees, I will not bring on you any of the diseases I brought on the Egyptians, for I am the LORD, who heals you” (Exodus 15:26).

Later, God gave the apostle Peter a vision that implied formerly unclean animals could be eaten: “Do not call anything impure that God has made clean” (Acts 10:15).

Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfil them (Matthew 5:17)

When Jesus spoke these words he was speaking to a Jewish audience. When Jesus died on the cross, He fulfilled the Old Testament law (Romans 10:4; Galatians 3:24-26; Ephesians 2:15). This includes the laws regarding clean and unclean foods.

The prohibitions and restrictions detailed in the book of Leviticus do not apply to Christians. Jesus Christ came to establish the New Covenant between God and His people. Romans chapter 8 shows how Jesus is the mediator of this new covenant which is superior to the old one and is founded on better promises. Entering the New Covenant is made possible only by faith in Christ, who shed His blood to take away the sins of the world (John 1:29).

We are no longer under the Law but under grace (Romans 6:14–15). The Old Covenant has served its purpose, and it has been replaced by “a better covenant” (Hebrews 7:22).

The laws in Leviticus are not separate, individual commands, but rather the whole of the Moses' Law is a unit, "which if a man do, he shall live in them" (Leviticus 8:5). This includes the laws of the temple and the sacrifices. You can't keep some or most. This answer is the entire basis of the Christian's faith in Jesus. In answering this question, I will present the purpose of the Law and the inadequacies of the law, and the expectations that Lawgiver Jesus has for his followers today.

Galations 3:11. Here Paul quotes Habakkuk to prove that the law does not bring about righteousness. This is confirmed in Galatians 2:16. The purpose of the law is not our salvation, but rather it serves as an preface to the coming Messiah. The purpose of the Law is to point to Christ.

²³But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed. ²⁴Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. ²⁵But after that faith is come, we are no longer under a schoolmaster. Galatians 3:23-25, KJV

Jesus is the Prophet spoken of by Moses in Deuteronomy 18:15 (See John 1:45). His role on earth was to "wrap up" the Law. This is why Romans 10:4 says that "Christ is the end of the law for righteousness." The law was already weak in that it could not provide the Spirit or righteousness through obedience in it. However, in fulfilling the law completely, Jesus is able to say, "It is finished." He did not fulfill it solely by obeying each of the individual laws, he also tied all the loose ends left in the inadequacies of the Law to absolve sin.

¹For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. ²For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. ³But in those sacrifices there is a remembrance again made of sins every year. ⁴For it is not possible that the blood of bulls and of goats should take away sins... ¹²But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God; Hebrews 10:1ff

I would like to emphasize that last verse, taken from Hebrews 10:12. In sitting down, Priest Jesus is contrasted to the ever-working priests of Leviticus. He is finished working, and the law is taken care of. Pleasing the Father never had to do with following the minutia of the law anyway. Micah 6:8. Today Christians walk in the Spirit, for "the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death" (Romans 8:2. See also vv 3-4). In a sense this is more difficult than following Moses' Law - there is no room for hypocrisy. The law of the Spirit means obedience in everything you do, not just in the 600+ commands in the Pentateuch. The Pharisees of Jesus' day were seemingly the most obedient of people, yet to them He said,

But go ye and learn what that meaneth, I will have mercy, and not sacrifice: for I am not come to call the righteous, but sinners to repentance. (Matthew 9:13)

Some Christians divide the Mosaic law into three components: Moral, Ceremonial, and Civil.

Moral laws apply to all believers at all times: the Ten Commandments, the Shema, etc.

Civil laws were for the governing of the nation of Israel. They may be valid today but the punishments listed with them might not apply to us.

Ceremonial laws were for the worship of the nation of Israel and are not binding on us. These include the animal sacrifices, which pointed to Christ the ultimate sacrifice.

That said, I have never seen a reliable method for sorting the 613 laws into these three categories without resorting to arbitrary divisions, so this may be merely an intellectual exercise with no practical application.

The typical reformed answer on this is that the Old Covenant is fulfilled in the the Death and Resurrection of Jesus and that we are now living under the New Covenant.

Lets look at this specifically point by point.

Leviticus 11:7-8 and Leviticus 11:11-12 have been fulfilled by by Acts 11:6-9

⁶I looked into it and saw four-footed animals of the earth, wild beasts, reptiles and birds. ⁷Then I heard a voice telling me, ‘Get up, Peter. Kill and eat.’

⁸“I replied, ‘Surely not, Lord! Nothing impure or unclean has ever entered my mouth.’

⁹“The voice spoke from heaven a second time, ‘Do not call anything impure that God has made clean.’ ¹⁰This happened three times, and then it was all pulled up to heaven again.

as far as Leviticus 11:19 is concerned this is pretty much the same line of thinking as above, its less explicit, but its essentially the same thing.