A number of important first generation Mormons, including Sidney Rigdon, one of Joseph Smith's closest associates, came from the Stone-Campbell movement. When the Mormons went to Great Britain in the first missionary effort, they found converts among the United Brethren. Brigham Young and his family were mostly former Methodists. In fact, a lot of the first Mormons were ex-Methodists. Enough, actually, that an early Mormon author found it useful to claim a continuity between Methodism's origins, with John Wesley, and the religious practices of the Latter-day Saints, writing, "spite of our few outward differences, there are no people so much like John Wesley and his early followers in spirit, faith and missionary energy ... as the Mormons."
Attention, these days, is more often placed on the connections to esoteric spiritualities -- Smith's practices of folk magic, e.g. -- but the relationship to Second Great Awakening evangelicalism was very strong. In many ways, it was defining. As John Turner writes in his bio of Brigham Young,
North Americans of diverse religious backgrounds converted to Mormonism, from skeptics to pious seekers, from universalists to practitioners of hermetic folk magic. The more religiously esoteric backgrounds of some Mormon converts, though, have sometimes obscured the deep influence of radical evangelicalism on early Mormonism.One group the early Mormons did not have a connection to, and did not draw converts from was Muslims. Yet, anti-Mormon writing from the 1850s through the 1890s portrays Mormonism, among other things, as deeply and importantly connected to Islam.
The real relationship between Mormons and evangelicals is rewritten, kind of wildly, into an imagined one between Mormons and the followers of the prophet Muhammed.
This is a wild association, having little to nothing to do with actual Mormons, actual Muslims, or the history of either group. It's almost a sort of free association, going from the reports of Mormonism's practice of plural marriage to stereotypes of Turkish harems, "conflating exotic national and racial identities to heighten the heretical nature of Mormon religion," as Tammy Heise of Florida State University writes.
In an article published in the Journal of Religion and Popular Culture, Heise shows there was a logic this slander, though. It had to do with distancing and dis-identifying, and also was a way for evangelicals, in particular, to make a claim to true Americanness. She writes:
By choosing Islam to articulate the dangers of Mormonism, anti-Mormon writers not only marked Mormon difference but also sought to exaggerate that difference by playing on religious, political, sexual, and racial themes. Connecting Mormonism and Islam allowed anti-Mormon writers to construct an alternate identity for Mormons that denied their white evangelical Protestant heritage and set them apart as a distinct people beyond the pale of full American citizenship.This was especially important to evangelicals because of the connection between themselves and the nascent movement of Mormonism. They saw Smith's faith as a kind of perversion of their own beliefs, a subversion of key values. Mormonism's perceived depravity seemed better, less disturbing, if it wasn't homegrown.
"Mormon depravity," according to Heise, seemed to be "masked by seductive duplicity as it attacked the nation from within its own borders and through the subversion of its most cherished institutions -- marriage, family, and republican government."
Heise's article, "Marking Mormon Difference: How Western Perceptions of Islam Defined the 'Mormon Menace,'" is an interesting study in religious bigotry, in polemical reactions to early Mormonism, and in how evangelicals, among others, positioned themselves against the Latter-day Saints, emphasizing real and constructing fictitious differences to establish the great distance between the two groups.
It sheds light on an interesting period in Mormon-evangelical religions, and how connections and contentious relationships were re-worked into complete estrangement.