How should we interpret Leviticus 18, 19? Leviticus 18 talks about sexual morality, whereas Leviticus 19 talks about food and what to eat and what not to eat. It is quite difficult to read these two passages together. Modern Christians seem to obey the sexuality commands in chapter 18, but not 19. But if we really believe in Bible is the word of God, we need to read them consistently, not intepreting one chapter according to one set of rules and another, another set of rules.

How should we interpret Leviticus 18 and 19? Should we obey both? Or should we obey none? If we obey only chapter 18, but not 19, what is the hermeneutical ground for this?
The Old Testament Law (Genesis-Deuteronomy) was effectively the constitution of the Israelite nation. It told their history, established them as a nation state, and gave them laws to obey individually and as a whole nation. The core of the law is the Sinai/Deuteronomy covenants. God made a contract with them that he would be their God if they would be his people, and they would show that by obeying the laws he set. Obeying the laws showed that they were God's people. But Christians are not citizens of the ancient Israelite state, and so are not bound by them. We look at the law like we look at the laws of other countries: sometimes interesting, sometimes containing laws we wish our own country had, and sometimes happy that we aren't bound by them.

All of God's laws are good, but they had purposes that do not apply to Christians. Some of them seem very strange, including the food laws which look very arbitrary, but even more some of the other ones, like not wearing clothes made to two types of fabric. God gave them these laws as lessons about how to show that they were different and separated from the nations around them.

We know that God no longer expects us to not eat any food we like because the New Testament specifically says so, such as in Matthew 15:16-20 and Acts 10. In contrast we know that God does still expect us to sexually pure, restricting sexual intercourse to heterosexual marriage, because the NT tells us that many times, such as in Romans 1 and 1 Corinthians 6-7. We don't obey the OT Laws because we're bound by them but because God has shown us that they were not culturally and time specific.