I'm an active member of the Church and consequently I think it's a good thing when BYU sports are successful. When in college I lived near BYU campus with my friends who were students and went to a bunch of games so developed an affinity. I'm just not a die hard BYU fan. I certainly don't cheer for BYU when them winning has a negative impact on Utah, but most of the time it doesn't. Also, when BYU is good it makes the rivalry better, beating BYU means more and has a more positive impact on Utah, etc.
So I like BYU in the same way I like the Baltimore Orioles. They aren't my favorite baseball team, but I like it when they win and do well. But I'll never cheer for them over the Giants or Padres. I suspect we all have teams that we cheer for outside of our favorites, BYU is simply one of those for me. That said, when they play Utah, I want them to die a slow painful death.