I like both teams, but the bad fans from both sides are horrible. And my observation is that the populations of bad Utah fans is about the same as the population of bad BYU fans. And it's those bad Utah and BYU fans that continue to feed off each other.
At a Utah game in 2002, I saw a Utah fan intentionally vomit all over a BYU fan because the opportunity was there. I personally reported him to the staff, helped the BYU fan clean up the mess, and the Utah fan was escorted from the stadium.
At a BYU game in 1993, I saw a BYU student with a paintball gun shoot a blue paintball point blank at a 10-12 year old kid's head because he was dressed in Utah gear at Cougar Stadium. I was too young at the time to really do anything about it, but I assume that a good BYU fan who witness the incident would have done the same as I did in 2002.
In the end, there is absolutely no difference whatsoever between the bad fans of each side, and the only way to avoid it is to avoid sporting events completely.
But neither sides' hands are cleaner than the others. That is the sentiment that you are asserting that I object to.