Like @The Jessiest, I'm a non-mormon, very liberal Utahn. I live in Draper, a suburb of Salt Lake, and I get along just fine out here. Granted, I grew up here, so I know how to handle the predominant culture, but once you learn to not let it get to you, this place is great. As an outdoors enthusiast, I am within minutes of skiing/snowboarding, hiking, biking, camping, etc. Seriously. It takes me less than a half hour from my doorstep to the chairlift.
I lived in Salt Lake proper a few years back, and I loved it (I was just priced out when I made the decision to buy). Salt Lake is not predominately mormon anymore, and actually, Obama won in Salt Lake County, as well as in Park City. So, if you are thinking Park City/Salt Lake areas, you'll receive much less of a culture shock than you would if you were to move to Utah County/Provo area.
And, if Park City is your final destination, I'd hardly think you'd experience any sort of religious cultural shock other than it's simply slower paced up there and you'd be surrounded by outdoorsy people.
I've been runnin' around here for 27 years now, and I've spent a lot of time in Park City with jobs and volunteer work. Feel free to PM me if you ever have other Utah questions or concerns.