This is a little belated but it's not often you see posts in this group.
I'm as liberal and as non-religious as you get and I have lived in SLC for quite a while. Contrary to some, I don't find it easy to live here in this political/religious climate. I live in the most liberal part of SLC and that's not saying much. SLC last I heard was 60% Mormon, 35% Catholic and the rest are everything else. If you have a strong desire to live with lots of secretive people who will never be honest or completely open you may find your place here. Park City is quite liberal but touristy and extremely expensive. You might look toward the other side of Park City to Heber City and a couple of surrounding towns which are a little more spread out and there are some liberals there; it's a fun area.
BTW, 95% of the rest of Utah is Mormon with the highest percentage in the Provo area where it's closer to 99.8%. The new NSA complex is on the outskirts of SLC if that means anything to you.
All in all, You may find nice people who are just what you are looking for but it will be a gamble in this state. When you do make contact with the natives it may work for a while but usually you will find yourself an outsider and less able to be honest as no one will be honest with you. It's my experience here working on the inside of the theocracy as well as outside. For example, one of the most recent posts in this group was by me asking for any input or ideas on voting for progressives or Dems in the June elections; I was asking for help and insight. Not one single comment... That is what you get when you live in this state 24/7 unless you fake it. I don't.
On edit: I did get two recs, one by you. Thanks... It's lonely here.
Good luck to you. But if you like the Utah surroundings you would do better living in NW Colorado and travel to your destination. All the best and sorry for the downer.