Both my parents actually went to Utah State, so I heard a bunch of taunting of BYU. When it came to choosing schools, BYU was never on my radar. I'm sure I could have gotten in (this was a long time ago and I had better grades and scores than a few of my friends who did go to BYU).
The interesting thing is that I think highly of BYU as a school, I just can't stand their sports teams. For me, the rivalry is less about the schools and more about the athletics.