But I have a suspicion if one is not LDS they would always be a little bit the outsider.
Definitely a possibility, though from my conversations with my non-LDS friends and acquaintances (as my view wouldn't be as helpful as I'm LDS) here it varies a lot by where you're living, the particular people you run into/associate with, and your own attitude. Salt Lake valley is 50% LDS, and thus 50% non-LDS, so it just depends. In our current house I end up talking to my nearby non-LDS neighbors more than the nearby LDS ones, just because personalities amongst the people in our particular cul de sac work out that our non-LDS neighbors happen to be more outgoing.
My work is about 50/50 as well. In my office we have a bit under half LDS, the rest being a mix of Catholic, Protestant, chill atheist, fedora Atheist, agnostic, Hindu, and Buddhist. If you venture outside of the Salt Lake Valley the numbers tilt sharply towards a much larger LDS majority.
Salt Lake City proper is the state's liberal stronghold, but the rest of the valley is pretty conservative. While outside of SLC there's not much liberal influence, the politics throughout the state are pretty heavily swayed by the predilections of the LDS majority, particularly in the realm of liquor laws.