I found this thoughtful essay by the late Father Richard John Neuhaus, published in a 2000 edition of First Things, helpful in trying to understand how to relate theologically to Mormonism. Excerpts:

Asking whether Mormonism is Christian or Mormons are Christians (a slightly different question) is thought to be insulting. “How can you ask that,” protests a Mormon friend, “when we clearly love the Lord Jesus as much as we do?” It is true that St. Paul says that nobody can say “Jesus is Lord” except by the Holy Spirit (1 Corinthians 12:3). But that only indicates that aspects of Mormon faith are touched by the Holy Spirit, as is every element of truth no matter where it is found. A Mormon academic declares that asking our question “is a bit like asking if African Americans are human.” No, it is not even a bit like that. “Christian” in this context is not honorific but descriptive. Nobody questions whether Mormons are human. To say that Jews, Muslims, or Buddhists are not Christians is no insult. It is a statement of fact, indeed of respect for their difference. The question is whether that is a fact and a difference that applies also to Mormonism.

More:

Beyond these doctrinal matters, as inestimably important as they are, one must ask what it means to be Christian if one rejects the two thousand year history of what in fact is Christianity. Christianity is inescapably doctrinal but it is more than doctrines. Were it only a set of doctrines, Christianity would have become another school of philosophy, much like other philosophical schools of the Greco-Roman world. Christianity is the past and present reality of the society composed of the Christian people. As is said in the Nicene Creed, “We believe in one, holy, catholic, and apostolic Church.” That reality encompasses doctrine, ministry, liturgy, and a rule of life. Christians disagree about precisely where that Church is to be located historically and at present, but almost all agree that it is to be identified with the Great Tradition defined by the apostolic era through at least the first four ecumenical councils, and continuing in diverse forms to the present day. That is the Christianity that LDS teaching rejects and condemns as an abomination and fraud.

More, below the jump.

Neuhaus continues:

Some have suggested that the LDS is a Christian derivative much as Christianity is a Jewish derivative, but that is surely wrong. The claim of Christianity is that its gospel of Jesus Christ is in thorough continuity with the Old Testament and historic Israel, that the Church is the New Israel, which means that it is the fulfillment of the promise that Israel would be “a light to the nations.” The Church condemned Marcion’s rejection of the Old Testament, and she never presumed to rewrite or correct the Hebrew Scriptures on the basis of a new revelation. On the contrary, she insisted that the entirety of the old covenant bears witness to the new. While it is a Christian derivative, the LDS is, by way of sharpest contrast, in radical discontinuity with historic Christianity. The sacred stories and official teachings of the LDS could hardly be clearer about that. For missionary and public relations purposes, the LDS may present Mormonism as an “add-on,” a kind of Christianity-plus, but that is not the official narrative and doctrine.

A closer parallel might be with Islam. Islam is a derivative of Judaism and Christianity. Like Joseph Smith, Muhammad in the seventh century claimed new revelations and produced in the Qur’an a “corrected” version of the Jewish and Christian scriptures, presumably by divine dictation. Few dispute that Islam is a new and another religion, and Muslims do not claim to be Christian, although they profess a deep devotion to Jesus. Like Joseph Smith and his followers, they do claim to be the true children of Abraham. Christians in dialogue with Islam understand it to be an interreligious, not an ecumenical, dialogue. Ecumenical dialogue is dialogue between Christians. Dialogue with Mormons who represent official LDS teaching is interreligious dialogue.

Finally:

As for the rest of us, we owe to Mormon Americans respect for their human dignity, protection of their religious freedom, readiness for friendship, openness to honest dialogue, and an eagerness to join hands in social and cultural tasks that advance the common good. That, perhaps, is work enough, at least for the time being.

That’s the gist of Neuhaus’s essay, but I encourage you to read the whole thing. I find nothing in it to disagree with, and much to commend.