Why don’t Christians need to follow the Old Testament Laws (especially the Old Testament Civil Laws) anymore?
Christians do not need to follow the Old Testament law because Jesus fulfilled the Law (Matthew 5:17). Jesus replaced the Law of Moses with the Law of Christ (1 Corinthians 9:21, Galatians 6:2). The requirements of the Law were met and the law that “was against us and stood opposed to us” was nailed to the cross with Jesus (Colossians 2:13-15 note: this passage applies to all kinds of laws, not just the Law of Moses). Paul tells us that we are not under law, but under grace is several places in Galatians (4:28-5:1, 3:23-25, 3:2-6, 3:10-11 and more). Jesus satisfied the requirements of the Law of Moses. One effect of this is that those who are in Christ are no longer under the Law of Moses, whether they are Jewish or not. Christians do not need to follow any of the Laws of Moses, not just the supposed “civil” laws (I do not believe that this distinction regarding civil law is a very useful one in any case). We know from Acts 15 and the Jerusalem Council and from the statement in Mark 7:17-19 regarding unclean food, and from the statements from Paul regarding circumcision, and from a number of other statements in the New Testament that the apostles did not consider Christians to be obligated by any of the laws governing the Israelites. In Colossians 2:16-17 Paul is specific with regard to Sabbaths and other Jewish observances that we are no longer required to observe them.
The verdict of the New Testament is clear that Christians are no longer obligated to observe the laws given especially to the Jews at Sinai. Of course, there were laws given to the Jews, such as do not kill and do not give false testimony which would still be in place in Christ, because such things are clearly ruled out based on what Christ and the apostles taught, but in this case, we are obligated because of the words of Christ, not because the laws were given at Sinai.