Always intervene when you hear campers put each other down. Never believe a camper who says, "It doesn't bother me."
In our lives we are either growing into the people we can become or putting energy into protecting who we are. We can't have both simultaneously. Camp is one of the few places where we can control the external environment enough to give children an extended opportunity to grow.
Too many stories of kids who wind up in great trouble start with the innocent name calling and the adults who ignored it when they had the chance to do something about it. Letting it slide by — even once — sends a message that you condone the behavior, or at the least that you'll only respond when it is extreme. It truly doesn't matter how skilled a counselor you are at intervening, just saying something about it being "not okay" or "un-cool" is enough to disrupt the flow of what is going on. Intervene consistently, and you'll establish a culture that does not permit this negative behavior. Who knows, doing so may also save a life someday.