The really curious thing is why didn't Bryan do so well out there in 1900?
Yeah, he went from 82.7% in Utah in 1896 to 47.3% in 1900. Weird.
Mormons voted as a bloc for Bryan in 1896 because, well, most of them were already Democrats. Things had changed by the turn of the century, though- the LDS leadership began a campaign to convert its flock to the GOP, cynically attempting to curry favor with the Republican administration in Washington. Mormons being Mormons, they went along, and by 1912 Utah was one of only two states carried by LDS-endorsed William Howard Taft.
Re: Bryan's collapse in the mining belt, silver had largely vanished as a hot-button issue by that time; as the national debate shifted from economics to foreign policy, his vote fell off in the west (with a corresponding increase in the cities of the Northeast).