I get asked this a lot (but not by Mormons). My first short answer is: "Yes and no; it depends on who's answering the question". If you belong to the Church of Jesus Christ of Latter-Day Saints, you'll say yes. If you're a Nicene Christian, you'll say no. That's because for Nicene Christians ( = anyone who traces their ecclesial tradition back through the Council of Nicea in 325 AD) trinitarianism is an essential component of true Christian faith; without it, you're not really a Christian. But if you're a Mormon, trinitarianism is not an essential component of true Christian faith; instead, it's where (in part) Nicene Christianity went wrong.
Oh, but you're not asking a Mormon or a Nicene Christian, you're asking me . . . in my capacity as a teacher of religious studies in a secular academic institution. In that case, my second short answer would be: "Well, what do you think? And why?" . . . in which case, we'd probably end up in the vicinity of the first answer, eventually.
But my third short answer, when finally cornered like a hunted beast, would be . . . "Yes" -- even though I also happen to be a Nicene Christian. Why? Because, by regarding trinitarianism as an (if not the) essential component of true Christian faith, Nicene Christians define what it is to be Christian in a way that by definition excludes non-trinitarian forms of Christianity.
Gnostic Christians in antiquity were riding in pretty much the same boat that Mormon Christians are today, it seems to me (though it was probably a good bit bigger, and the "orthodox" boat a good bit smaller, than today). In fact, whenever we study Gnostic Christian texts in my courses, it's my Mormon students who tend to resonate with them on a personal level, because some things in them dovetail nicely with Mormon doctrines in ways that they don't for students with other faith commitments. As a scholar of religion, I don't see any reason whatever to deny the label "Christian" to various Gnostic or Mormon groups that clearly regard(ed) themselves as Christians; the deciding factor in favor of calling them Christians is that some form of belief about Jesus of Nazareth is essential to them as religious persuasions.
On the other hand, as a Nicene Christian, I do find it jarring to accept ancient Gnostics and contemporary Mormons as fellow Christians. Instead, personally, I do want to tend to classify them (in a knee-jerk kind of way) as non-Christians, which means that I would rather identify Gnosticism and Mormonism as world religions, alongside Buddhism, Hinduism, Judaism, Islam, Sikhism, etc., and (yes) Christianity. Nevertheless, even in Nicene Christian contexts (e.g., in church), I also do tend to speak (in spite of myself) (when the subject comes up) of Mormon Christians and Gnostic Christians in much the same way as I would Catholic, Orthodox, and Protestant Christians.
(I seem to recall that Old Uncle Walt [Whitman] wrote an impressive couple of lines somewhere celebrating inconsistency.)
Professionally (as a religion scholar), my final answer is that of course they're Christians . . . although (as a religion teacher) I'd rather help you figure out how to answer the question for yourself instead of getting an answer from me. Confessionally (as a Nicene Christian), my answer has to be: "I'm not so sure" . . . the very same answer I'd have to give, by the way, regarding some forms of (so-called) Christian fundamentalism, though for different reasons. But that "I'm not so sure" is not the same thing as a (properly Nicene?) "No". Unlike such a "No", it's an answer that refuses to let the last word be already said, an answer that's only on the way there (wherever "there" is), still in the middle of things, one that has yet to arrive. I'm still asking the question myself, even though I've already answered it (in a way, however, that I find to some extent questionable).
