I seldom feel any hate for an actual team or institution, it is always the fans I find annoying. Like ute fans. I don't actually have any real dislike for the university of utah or even the players on any of their teams, but they have some of the most obnoxious clowns for fans that exist anywhere.
My son is currently being recruited pretty hard by utah in a sport while BYU has not paid much attention to him yet, so I could possibly find myself supporting the utes, at least his team in his sport, if he winds up there and I wouldn't have any cognitive dissonance doing it. But I don't think I could ever like their fans in general regardless of if my son is one of their athletes.