Matthew 18:15-20 give us one of the classic biblical texts on confrontation. Once again, it is likely teaching that has been shaped in the context of the later church, since there was no church at the time of Jesus’ ministry. But this doesn’t diminish its truthfulness in any way. If a brother or sister, someone in your local church, does something wrong, go to them first privately.
We notice a couple things right off the bat. First, this teaching is not primarily aimed at the relationship between Christians and non-Christians. It seems primarily a matter of discipline within the Christian community. A second question is whether Matthew means sin in general or when a person sins “against you,” as some manuscripts of the New Testament say. The earliest manuscripts simply say, “if your brother sins.”
It isn’t a small point. There is a huge difference between going to talk to someone one-on-one because they have wronged you and going to talk privately to someone who has done something wrong in general. My sense is that Matthew is talking about sin in general, not just a sin against you.
At this point some cultural elements might come into play. After all, Jesus taught ancient Jews in Galilee, and Matthew wrote to ancient Christian Jews probably somewhere in Palestine. How you go about engaging other people on sensitive issues is not a timeless aspect of human nature or culture. The connotations of various actions vary from place to place. 
So it would not only be silly but counterproductive simply to assume that the “rules of engagement” in Matthew 18 should be applied in all times and all places in exactly the same way. For example, in the American context there could be many situations where it would not be wise or appropriate for a woman to confront a man privately or vice versa, especially if the other person had sinned against you in a sexual way.
Even in Jesus’ day this teaching would not have been intended to be absolute. If you had asked Matthew’s audience whether a woman should confront a man who had sinned, they almost certainly would have specified specific people who would be more appropriate to do so. It is a general principle—those who do wrong should be encouraged to stop. One-on-one private confrontation is often a great place to start, but it may not always be the best place to start.
Indeed, in the litigious world in which we live, it might often be wiser to start with Matthew’s second step: “If they will not listen, take one or two others along.” This is especially the case if they have sinned specifically against you. If it is wrongdoing in general, perhaps it would be wise for leaders to be the ones to confront, rather than just anyone. And at this point we might snap back to remember that in Matthew’s narrative, Jesus is talking to the disciples here rather than to the crowds...