I definitely had friends who were Ute fans and were exactly as you describe during the 80's: they followed BYU more than Utah, just to cheer against BYU and then hopefully talk some trash if BYU lost.

That said, those same Ute fans went from annoying to insufferable when Utah actually started winning on their own. And so I find myself cheering against the Utes specifically because of those obnoxious fans. I don't have anything against the university or the athletes - just their terrible jerkwad fans that I can't stand.