coaches needing to be members of the church, I can also see some wisdom in it. There are a couple of reasons: 1. A head coach that is a member of the church is less likely to try to discourage an athlete from serving a mission or show disappointment when one makes that decision, 2. Having someone be a member of the church is one more buffer on their conscience when they are tempted to break rules in high pressure situations in order to succeed, and 3. If the women's XC and track coach gets caught in a major cheating scandal the publicity and impact are lot less than if the FB or BB coaches were to do it.
Of course, there are people not of our faith who have just as much integrity as any member. And there are members who have made big mistakes at other institutions. I'm simply saying with #2 that when the temptation to make a big mistake arises a church member will know it will reflect poorly on BYU and the church. And they're more likely to care about that in addition to their personal integrity.