I've mentioned elsewhere, including on this post, how I grew up a Utah fan and then became a BYU fan when I went to college there. Maybe that makes me less die-hard than some, and I certainly don't have the expectations some do (partly because my years at BYU and birth of my fandom corresponded with pretty weak football teams).
The one thing I will say is that it's become easier and easier to be a fan of both. Living out of state and with the two teams generally not in competition for any meaningful accolades, it's getting easier and easier to root for each team's success without it coming at the expense of the other.