Regarding the status of the LDS faith as a "Christian" religion, there is a sense in which the dispute is more verbal than genuine. To put it simply, each party in this dispute is defining the term "Christian" differently. When LDS people say they are "Christian" they are defining the term differently from Protestants, Catholics, etc., and vice versa. Each group has a distinct theology that overlaps with the others in some respects, but is also different. What's more, each group admits these differences. So the question about whether Mormons are "Christian" is somewhat ridiculous. As Mormons understand the term, they are Christians. As the other groups understand it, they are not.
But that's not the whole story. The resistance that members of the traditional denominations have shown toward Mormons calling themselves "Christian" stems from their suspicion that Mormons want to downplay important theological differences between historical Christianity and Mormonism, in order to appeal to potential converts. Members of traditional Christian denominations think of themselves as sharing a core theology (a common "denominator") that links them and distinguishes them from other groups. They interpret Mormon attempts to label themselves "Christian" as attempts to include themselves among the traditional denominations, even though they admittedly reject the theological doctrines that link them together.
If this is true, the resistance is understandable. The LDS Church regularly distances itself from groups using its label while misrepresenting or deviating from Mormon doctrine, and rightly so. If a splinter group calls itself "Mormon," the LDS Church has every right to distance itself, and if preserving the integrity of its traditional label is essential to that purpose, there is no objection to their doing so. By the same token historical Christians want to distinguish themselves theologically from Mormons and they see exclusive control of their traditional label "Christian" as critical to this effort.
Unfortunately, the term "Christian" is overly broad. It also refers to ideals of conduct and virtue and to a theological and historical connection to the person of Christ that Mormons can legitimately claim as their own. Is there a solution to this interminable (and irritating) debate?
If members of the traditional denominations are wrong about the Mormon public relations strategy, this dispute can be settled (assuming both sides can overcome self-righteousness). Each side admits theological differences and that their understanding of the term "Christian" is different. However, if they are correct about the Mormon public relations strategy, there is no foreseeable end to all this wrangling.