"you will be fine, just man up because everyone says swears sometimes"
to
"well, yeah, there are really horrible people in my fanbase, but I won't do anything to you! And I'm willing to put up with the other team praying to their God, so you should be willing to put up with all of our antics!"
The two fanbases don't even compare. BYU is likely the tamest of all fanbases in major college football. The bad apples are few and far between. There are kids and elderly everywhere in our venues. It's likely that more than 90% of our fanbase doesn't drink. So yeah, I think the experiences you'll get as a visiting fan at BYU vs. at Utah (or at any other state school, for that matter) will be demonstrably different.
I don't think Utah fans are any different than any other state school when it comes to their fanbase, except on rivalry weekend, when the anti-Mormon element intensifies things. And at that point, I think it's fair for someone to be cautious about subjecting themselves or their loved ones to that kind of behavior. I would likely take my kids to an ordinary Utah game (well, except I don't cheer for the Utes) if we sat in the west stands or in the visitor's section. But I would never take my kids to a rivalry game at Utah.