Question: "Do Christians have to obey the Old Testament law?"
Answer: The key to understanding this issue is knowing that the Old Testament law was given to the nation of Israel, not to Christians. Some of the laws were to make the Israelites know how to obey and please God (the Ten Commandments for example), some of them were to show them how to worship God (the sacrificial system), some of them were to simply make the Israelites different from other nations (the food and clothing rules). None of the Old Testament law applies to us today. When Jesus died on the cross, He put an end to the Old Testament law (Romans 10:4; Galatians 3:23-25; Ephesians 2:15).
In place of the Old Testament law, we are under the law of Christ (Galatians 6:2) which is to, “Love the Lord your God with all your heart and with all your soul and with all your mind. This is the first and greatest commandment. And the second is like it: Love your neighbor as yourself. All the Law and the Prophets hang on these two commandments” (Matthew 22:37-40). If we do these two things, we will be fulfilling all that Christ wants for us to do, “This is love for God: to obey his commands. And his commands are not burdensome” (1 John 5:3). Technically, the Ten Commandments are not even applicable to Christians. However, 9 of the Ten Commandments are repeated in the New Testament (all except the command to observe the Sabbath day). Obviously, if we are loving God we won't be worshipping other gods or worshipping idols. If we are loving our neighbors, we won't be murdering them, lying to them, committing adultery against them, or coveting what belongs to them. So, we are not under any of the requirements of the Old Testament law. We are to love God and love our neighbors. If we do those two things faithfully, everything else will fall into place.