Christians who believe that the Bible is true because it is God's Word have an uncomfortable relationship with the Law of Moses delineated in Exodus, Leviticus, Numbers, and Deuteronomy. In fact, there has been substantial diversity of opinion about how to regard it going back to the apostles themselves (see Acts 15:1-35; Rom. 14:1-15:13; and so on).
This difficult question stems from the often difficult-to-reconcile words of our Lord Jesus himself. Undoubtedly Jesus believed that what we call the Old Testament was the Word of God (see, e.g., Matt. 5:17-19; John 10:34-35). So it is not surprising that in Mark 7 Jesus says that the Fifth Commandment (to honor one's father and mother) isn't just Moses' word, but God's Word. But a bit later in the same chapter Jesus declares all foods clean, directly contradicting Moses' word in the same Book of Deuteronomy.
Does that mean that the food laws in the OT aren't God's Word? No it doesn't, but something has changed. But what? And how do we apply the change to the rest of the Law?
This isn't just an academic question. It is frequently brought to bear on the hot-button issue of homosexuality. Some argue that homosexual activity is wrong in part because of Old Testament Law, and those who engage in it or endorse it are sinning. Others argue that that law was abolished by Christ's work on the cross like the food laws were and that those who insist on it are legalistic Pharisees. Obviously, since the judgment of God is at play here, the stakes are high for both sides.
We can look at the problem of the Law from a number of angles, but the one that I think is most useful comes from the New Covenant prophesied by Jeremiah and enacted by Jesus' blood: God says, "I will put my law within them and write it on their hearts and minds" (Jer. 31:33).
Jesus said that he did not come to abolish the Law (Matt. 5:17). He came to take the written Law that mandated behavior from the outside and infuse it into a person's being so that it welled up from the inside. Instead of being written on stone or papyrus, it would be written on the conscience of the person him- or herself. Rather than keep jamming square pegs into round holes, Jesus came to make square pegs round by bringing people to life through the Holy Spirit.
But when the Law of Moses moves from the outside of a person to the inside, the Law changes in one of two ways.
Sometimes the Law is intensified when it is written on someone's heart. For example, Jesus said, "You have heard that it was said, 'Do not commit adultery' [Ex. 20:14]. But I say to you that whoever looks at a woman to desire her has already committed adultery with her in his heart" (Matt. 5:27-28). So as long as the Law was on the outside the focus was on not physically having sex with someone else's wife. But when the Law moves inside the focus is on not even imagining committing that sin. Now if one keeps from imagining committing adultery, one isn't liable to commit it physically either—that action is still wrong. So writing the Law on the heart actually makes some Law more rigorous than it was before; it strengthens rather than nullifies the old commandment. All the sexual laws (including homosexuality, incest, bestiality, premarital sex, and so forth) fall into this category.
But other times physical requirements of the Law disappear when the Law is moved into the heart. The food laws are an example. The food laws were to keep people from making themselves "unclean" with "unclean" food. If we take that concept from outside our bodies into our hearts and minds, what does it mean to keep ourselves "clean" within? Being inwardly clean entails putting to death "evil ideas [specifically pertaining to] sexual immorality, theft, murder, adultery, greed, evil, deceit, debauchery, envy, slander, pride, and folly. All these evils come from within and defile a person" (Mark 7:21-23). So the way Christians who have the Law written on their hearts keep the food laws is not by avoiding "unclean" foods but by avoiding unclean thoughts. The physical foods themselves are irrelevant.
So when you read the Old Testament and wonder if a given instruction applies to you, the answer is always yes. But the important follow-up question is, "How do I keep this command in my heart and mind?" That may remove the physical obligation or it may reinforce it. But inwardly we are still to keep it.
This is real Law-keeping. "For a person is not a Jew who is one outwardly, nor is circumcision something that is outward in the flesh, but someone is a Jew who is one inwardly, and circumcision is of the heart by the Spirit and not by the written code. This person's praise is not from people but from God" (Rom. 2:28-29).