Like most Mormons, my problems with the Democrat Party begin with abortion. Mormon Democrats (like J. Crew) like to tell you that various old-fogey church members are Democrats. Yes, and so were most slaveholders. Parties change, and the post-Roe Democrat Party is not the same it was before.
Mormons used to vote Democrat in huge droves. The solid majority Republicans enjoyed after the Civil War made it so the national officials who persecuted polygamists were Republicans. As a result of this, and because Utahns were westerners who wanted cheap money, Utah often voted Democrat in the past. As recently as 1964, Utah went for Lyndon Johnson instead of the man that (if time machines, corpse reanimation, and gay marriage were realities) I would marry, Barry Goldwater. Goldwater was a Republican's Republican, and the argument that Mormons are anti-Democrat because they are anti-Socialist takes a hit when you realize Utah voted for Franklin Roosevelt's New Deal four times and for Johnson's Great Society.
The elections of 1968 and 1972 have Utah going for Nixon, but not in greater numbers than the surrounding states. By 1976, the first election after Roe v. Wade, Utah went Republican more than every other state in the country (62%). Utah was again the most overwhelmingly Republican state in 1980 (73%), 1984 (75%), 1988 (66%), 1996 (54%), and 2004 (72%). In 2000 Utah was within one percentage point of the most Republican state (Wyoming, 68%), while in 1992 there were other states that were more Republican, but Utah was the only state where the Democrat came in third place.
I submit to you that the "solidly Republican" Mormon majority is really just solidly anti-abortion. The Democrat Party's embrace of abortion (and its logical conclusions of euthanasia and infanticide) has created the Mormon Republican majority.