... are bunched together like at Utah and USU. Easy to play up the stereotype (occasionally earned but vastly overplayed) that BYU students are haughty, elitist, hypocrites who feel they are better (even more righteous or favored by God) than anyone else. That factor is really egged on by the anti-LDS folks at and around each institution. Especially for the more publicly polite among them, hating on BYU sports acts as a vehicle for them to release their disdain for the Church and/or Mormons in general. One could argue that "hating BYU" is a type of therapy for these largely repressed emotions.
That's really feeding much of this, and the sports angle just gives voice to the undercurrent reasons mentioned above. But doing away with BYU sports (as some suggested Uchdorf might have been alluding to with his "Stop It" talk in GC) won't fix most of their feelings.