(This started out as a comment to this post, in reply to Adam G., but became so lengthy that I decided to make it a post of its own. For purposes of this post, “LDSC” refers to the LDS Church; “CC” refers to the Catholic Church; and “NLDS” refers to non-LDS Christians.)
Why do the non-LDS churches reject the LDS Church as non-Christian? I suggest that it’s based on things which strike at the heart of the other churches: Namely additional scripture, new revelation and ongoing, authoritative prophecy.
The NLDS had gone through centuries of conflict over precisely these issues: The true content of the scriptures and the weight, if any, to be given to non-scriptural authorities. In other words, how do Christians know what to believe? The Reformation may have started out as a reformation, but it finished, i.e. the rupture was made complete, over issues of authority. The Protestants could not be welcomed back without submitting to the teachings of the Popes and the Councils, the authority of which the Protestants by-and-large rejected.
The CC asserted that it was of the very essence of the Christian Church to have extra-scriptural authority, as well as Apostolic succession and a valid priesthood and sacraments; and virtually all the Protestants rejected precisely those things, asserting that the only essential things were faith and the Bible. Note that these things were held to be essential to the Christian church, such that groups which held the opposite view, to that extent were held not to be true Christian churches. Thus the CC was held not to be the true Church of Christ but the whore of Babylon; and the Protestant churches were held not to be true Christian churches but mere gatherings of people who might profess faith in Christ but who reject the very Church he had founded, as well as his lifegiving sacraments.
Fast-forwarding to the appearance of the Mormons, where do they fit into this divide? To the Protestants they smack of papist extra-scripturalism and hoodoo (i.e. sacramentalism); and to the CC they are yet another Protestant, or at least Protestant-like, sect which rejects the Church of Christ and sets itself up as its own magisterium.
The Protestant distrust of Mormonism is not a new stick specially cut to beat Mormons with, but is based on the same principles which caused them to reject the CC and go their own way in the first place. And the CC’s rejection of Mormonism is based on the same principles by which Protestant groups were judged to be not genuine churches but mere agglomerations of people claiming to be followers of Christ.
The LDSC, seemingly, comes in hoping to please both sides, but instead reminds both sides of each other. This is the reason it “catches it from all sides”, so to speak.
I submit that this was not surprising to Joseph Smith. He knew how Protesants viewed Catholic principles, and perhaps knew how Catholics viewed the Protestant tendency to continually re-interpret the Gospel. He must have known full well that both sides would react with revulsion. His attitude seemed to be basically, “bring it on”.
The modern LDSC, I suppose, having been around now for one and three-quarter centuries, wants to say, “Come on. We’ve been here this long and have shown ourselves to be good people. We’re not persecuting you or corrupting your youth. Accept us already.” There has been such a liberalizing and democratizing trend among all Christians, that Mormons perhaps have been encouraged to expect this to happen. Indeed I think that to a large extent it has. Which makes the holdouts appear all the more bigoted and unreasonable. (The holdouts, by the way, happen to be the more conservative adherents of their various faiths.)
The difficulty, though, for many Christians, is that the LDSC hasn’t changed the principles upon which it was founded, which formed the basis for their initial negative prejudices. It still insists on calling its additional scriptures scripture, and still holds open the possibility of new and ongoing revelation leading God-knows-where: Even if Protestants could reconcile themselves to existing LDS doctrine, that doctrine is still liable to change or be added onto (unlike Catholic doctrine, to which they have had five centuries to acclimate themselves). And the Catholic objection to considering the LDSC a genuine Christian church is unchanged as well: No Apostolic succession, valid priesthood or sacraments, especially the Mass.
So there we are!
All of the foregoing has addressed the question of whether the LDSC is a genuine Christian church. Whether individual Mormons are truly Christian is a separate question, which I have answered for myself here and here (see also this post): Basically, I can’t see much ground for denying that Mormons are Christians in some sense, i.e. by the broadest possible definition, and for that reason won’t quibble about referring to them as Christians; even though by a stricter and what I consider the most proper technical definition, I would say they are not (due to most likely not receiving valid baptism — a criterion which I apply to members of some other Christian denominations as well).
I admit I have a hard time seeing how Protestants can justify denying the title of “Christian” both to Mormons and the LDSC. The Catholic arguments are of no use to them, and I don’t see any objective Protestant standard which clearly excludes them, the Protestants themselves having abandoned the Apostolic succession and undermined the idea of an authoritative interpreter of the scriptures. Thus all they have in my view are subjective opinions (which, however, they are entitled to after all).
That’s what they get for leaving the One True Church!
In closing I will just suggest that drawing lines of division is not always an act of hatred. For example from the LDS point of view, it’s necessary to assert the Great Apostasy in order to make known the need for restoration. If all this is true, then telling people about it is an act of love. By the same token I believe that for many Protestants, it’s necessary to insist on the non-Christian (as they see it) nature of the LDSC for the sake of not giving false comfort: No one would be happier, I have no doubt, if Mormons were true Christians or were to become true Christians; but they can’t be told of the need to become Christian without also being told that they are not so currently. And for a Catholic, too, the succession, priesthood and valid sacraments are so precious and essential, that to treat them as if they were not needed by Mormons (or Protestants) to be a true Christian in the fullest sense, would be inexcusable and certainly not an act of love.