The ironic thing is that up until recently, Mormons proclaimed no unity with other Christians. Through the 70s, Mormons were, by their own definition, a separate people which finds more in common with the Jews than with any other Christian church. As Mormonism considered itself the restoration of the truth which was lost by unrighteous Christianity; polluted by the Great Whore, the Catholic Church; and whose ministers are paid pawns of Satan.
Mormonism of the 1860s and 70s could be clearly argued to not be Christian, with neither side disagreeing. Not that Mormonism had rejected Christ, but that the doctrine had so clearly evolved beyond anything reconcilable. From its roots as what can only be described as a cult founded by a confidence man, to its open practice of polygamy and adherence to self-proclaimed prophets, it had made enough of a break from its Protestant roots that it was in a separate category by itself. Blood oaths, polygamy, polytheism including the doctrine of God = Adam, to name a few of the doctrines on the extreme side which could justify other Christian denominations from wanting to completely disassociate with Mormons. Mormons of this era clearly saw themselves as the inheritors of original Church and believed that that other Christians were deceived at best and evil at worst.
Brother Brigham was the perfect man for holding the church together after Smith’s death, and while he also inherited Smith’s direction of theology, he lacked Smith’s charisma and failed to persuade his fellow leaders who rejected his more radical teachings, including the aforementioned Adam is God doctrine. Had that school of continued, there is no doubt that there would have been a complete break. However, once the rule of bureaucrats took over, along with the loss of the hearing the world of God spoken in the first person, the desire to be liked by the outside world eventually won out.
By the time the 1990s rolled around, the trend to appear mainstream had completely taken over. Under the leadership of Gordon B. “I’m not sure we still teach that” Hickley, it accelerated faster including such things as the now-aborted “we’re not Mormons” phase or the even less known attempt to address its Godhood to be more similar to mainstream Christianity. As the great divide between “us” and “them” is still clearly “Mormons” vs. “everyone else” and non-Mormon Christians fare no better in the hereafter than Muslims, Buddhists or atheists, and as these principles haven’t changed, there is no indication that this movement is anything more than a calculated PR move.
People make the mistake of looking to the Book of Mormon to see differences. When Smith wrote or helped write that book, he was still very classic Protestant. It wasn’t until five or six years later when he wrote the Book of Abraham that his theology had evolved into polytheism, which further expanded into “we-can-be-gods-too”theism of the 1840s.
As the Mormon church as not yet officially disavowed any of the advanced theology, other than Young’s Adam is God adventure, I think there is enough on the books to make an argument that Mormonism has moved beyond its roots sufficiently to be in new territory. However, as the church seems to be unwilling to maintain its extreme positions, and as scholarship is rabidly demonstrating the human authorship of what had been accepted as divine origin, I see Mormonism headed further back into mainstream Christianity.