Contrary to ignorant belief, mormons do practice modern medicine, they do not make up 90% of Utah's population and the University of Utah has a very good medical program. You'll need to get solid grades throughout undergrad to get into the medical program though as it is very competitive.
But I still highly recommend the U of Utah. I have yet to feel any regret for my decision to go to school here, almost everyone I've met is passionate about skiing/snowboarding and they're generally really chill people. In fact the only problem about Utah is having to listen to idiots who live in other states talk about how there's no parties or hookups because everyone here is mormon.