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
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;
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)