One reason Democrats may be more anti-Mormon than Republicans is that Democrats, on average, are more secular. Devout Protestants, Catholics, and Jews may be more tolerant of Mormonism because they understand from firsthand experience the comfort and strength that religious commitment brings. Many secular Democrats, by contrast, may start with the assumption that religious orthodoxy produces irrationality and intolerance.
But Mormons have long had a history of worrying about the fusion of church and state when the church isn't theirs'. Alas, their current crusade against the civil rights of gays – funding campaigns as far away from Utah as Maryland – casts them in a different light, that of persecuters.