We see consistency in the NT with all of these laws found in Leviticus 18. Incest, idolatry, adultery, and homosexuality are addressed. Jesus actually raises the bar on many of these laws from the OT. He famously declared adultery to be a sin inwardly as well as outwardly.
The controversial piece in Leviticus 18 which would crop up many times in the NT is found in verse 5.
Follow the practices and the laws that I give you; you will save your life by doing so. I am the LORD.”
Leviticus 18:5 GNB
The Pharisaic opponents of Paul quoted this verse to try to justify the stance that obeying the law fulfilled God’s will and that they would be saved in the end. We read Paul attack this theory in Galatians 3.
Now, it is clear that no one is put right with God by means of the Law, because the scripture says, “Only the person who is put right with God through faith shall live.” 12 But the Law has nothing to do with faith. Instead, as the scripture says, “Whoever does everything the Law requires will live.” 13 But by becoming a curse for us Christ has redeemed us from the curse that the Law brings; for the scripture says, “Anyone who is hanged on a tree is under God’s curse.”
Galatians 3:11-13 GNB
The law cannot bring justification. It can only show us the fact that we are sinners. In bringing forth the law, God showed us that we cannot measure up to His standard of holiness in our flesh alone. Paul argues that keeping the law (through the Holy Spirit) is the fruit of our Salvation by faith, not a means of earning our Salvation.
This interpretation of Leviticus 18:5 makes much more sense when read in context with what’s going on in Israel’s history. God gave them this law after He had rescued them from Egypt and established His covenant with them. The context does not indicate it was a moral standard they must reach in order to be saved spiritually. God knew they could not uphold it anyway. In the end, the law proved that all we can earn in this life is death and we need something much greater. Praise God He sent us Jesus Christ!