My parents taught me that an honest question deserves a well thought-out and thorough answer. As the child-full-of-questions, they carefully explained life, the universe, and everything when I asked (even when they were to the point of exasperation). Gosh, I'm thankful for their example.
My friend recently posted the following on Facebook (here's the link: http://www.lds.org/new-era/2011/08/the-only-true-and-living-church):
And I told him I would give him my response. So, without further ado...
I think what you're asking is, "Why do Christians support Romney when he doesn't believe most Christians are part of the 'true church'?" Completely legitimate question, but let's start with some background.
What do I think about Mormon's Exclusive "Church"?
Though Mormons believe they are Christians, most Protestants and Non-Denominational (e.g. "Bible" churches) Christians don't believe they are. Protestants and Non-Denoms believe that one becomes a Christian by faith alone (believing that God/Jesus is who he says he is and did what he said he did), while Mormons believe that works are also a part of becoming a Christian. This is obviously a broad-stroke picture, but the point is that they don't agree with traditional Christians.
Mormon theology is based on the Holy Bible and the Book of Mormon. Protestants and Non-Denoms (and probably Catholics, but I'm not certain) don't use the Book of Mormon because it doesn't meet the requirements for the Biblical canon. As you probably know, there are a lot of gospels (think "The DaVinci Code"), but only some are part of scripture. Some of the requirements are the following: that they should be primary sources, written close to when the events happened, and verified by the rest of scripture. Some problems with Joseph Smith's revelations are that they were to one man (privately), much later than the rest of scripture, and they contradicted the other parts of scripture. (There's a lot more on this in the book The Case for Christ by Strobel.)
With all of that said, I don't see why there couldn't be Christians who are Mormon. It would be silly to think that every person adheres perfectly to every tenet of their denomination. I think it's very likely, given that they have the same Bible that I do, that some Mormons have the same saving faith that I have. I'm not in any sort of position to say that specific people are or are not Christians; God and the person are the only ones certain of the state of a person's soul.
So, if a person believes in Jesus' saving work on the cross, then I believe they are part of the Church (universal). If they think that I'm not part of the Church since I don't go to their LDS church, then I think they are misled. But, knowing who is and who isn't part of the Church isn't a requirement for salvation, so it's not essential.
What does the responsible Christian do if they don't (spiritually) agree with either candidate?
So Romney doesn't think that I'm a Christian. Well, I suppose that doesn't matter so much to me. I disagree with both candidates on different (Christian) issues; neither lines up perfectly with my theology (and I doubt any candidate ever will... unless I ran for president... Lord, help us all).
The responsible Christian will consider the issues most important to him or her and then find the candidate that most aligns with those issues. Honestly, you could substitute "American" with "Christian" in the last sentence, because the general principle is the same, even if the issues are different. I think it's less about rooting for someone on your "team" and more about finding someone who you agree with. We get so caught up with labels (and I do think that labels are helpful in some situations), that sometimes we can miss glaring discrepancies. It's important to know the facts. It's also important to know what you believe and why you believe it. This is what my friend was getting at (I think), and I agree with him (and I say "way to go" for holding me accountable). You know who you are -- thank you.
EDIT: I suppose the main idea here is that I'm voting for my president, not my pastor (an important distinction). America's not a Christian nation, and so I don't expect the president to play the pastor role.