If it's Clinton vs. Trump after an Obama vs. Romney election, Utah will swing hard to the Dems. Nowhere near enough to flip it, but probably at least 15 if not 20 points (in terms of margin of victory).
It's not so much what Trump has said about the LDS Church, but what they've said about them. The LDS Church has made it clear that they are not getting behind Trump as a candidate, and as a result, Trump has continuously polled terribly in both general election matchups in the state (still winning, but usually with single digits and loads of undecideds). He gets third in most primary polls there, even while ahead everywhere else, and he still managed to lose Nevada's Mormon areas overwhelmingly even though he walked away in the rest of the state.
There are a couple explanations why, but these articles give a glimpse:
http://ldsmag.com/the-real-trouble-with-trump/http://www.deseretnews.com/article/865643612/Mormons-and-the-Trump-proposal.html?pg=allMostly it comes down to two things:
1) Trump is seen as not truly believing in the principle of freedom of religion, as evidenced by his "stop the Muslims" policies, and Mormons are concerned their way of life might be threatened as a result.
2) Trump is seen as an immoral person himself who promotes adultery, gambling, drinking, etc. A large reason that the Mormons have been so loyal to the Republicans over the years is specifically because the party is the one seen as more likely to denounce and quell these behaviors, rather then promote and indulge in them.
