It was not until the mid- to late-1970s that the Democratic party fell out of favor among Utah Mormon voters.
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Thius was becasue Jimmy carter was POTUS at the time and he presured them to change their racist stance against blacks...
In 1978 they introduced a nbew doctrine for political expediency and told the sheeple to hold their noses and vote for those evil republicans who had rejected the god-man George Romney twice...once in 1964 and again in 1968..
What were the numbers on Utah votes for Carter in 1976 ???
Ford took Utah over Carter 62-34% [nationally, Carter beat Ford by 2%]
So what you said wouldn't hold true unless Carter was pressuring them during the campaign -- which I don't believe he did.
It's possible that since some of the press was portraying Carter as a "born-again Christian" in the '76 race, that Lds voters, which took a much harsher anti-Christian stance at that time led by Lds apostle Bruce McConkie, didn't want to "hold their nose" and vote for a "born-again Christian." [Of course, we discovered more of Carter's faith-based beliefs as the years went by]