It was tougher at first, but eventually our relationship grew to a point that it was more significant than the rivalry. Congratulate them when they win. Don't rub it in their faces when BYU wins. You can probably even agree to some extent on some of their opinions. Some BYU fans are hypocrites (same for Utah). Not all Utah fans are classless.
Don't let them walk all over you. Confront them directly about it if it bothers you. But recognize that being nice to them is what should set BYU fans apart. Its what we should be all about. If you don't then you are just reinforcing their opinion.