It's easy to cheer for Utah when BYU is winning most of the games. I think things started to shift when Utah became much more competitive in the McBride years. The first 31-34 TV ads were funny - until it happened again. Then BYU fans were much less amused.
But I agree about cheering for Utah. I watched Utah in the final four at a Ute friend's home and cheered for their their entire NCAA tourney run.