Now these things do influence decisions, but most people have things backwards. Our professed (or labelled) identities are no sure predictor of how we will act. Humans are not primarily thinkers. We are usually quite inconsistent. Our real identities are revealed by our patterns of behavior and often have little to do with our professed identities (or the identities given us by the labels of others).
Is Mormonism a theological cult? Certainly the official beliefs of the Mormons are unorthodox by historic Christian standards. Jesus was not on equal footing with Satan when God presented his plan of salvation to them both. It stretches the limits of the mind that The Book of Mormon is "another" testament revealed to some of the 10 lost tribes of Israel (read Native Americans) and delivered to a man who found golden plates in the 1800s on the frontier (that have now conveniently disappeared).
But sociologically, in terms of how how he behaves as an American, Romney seems within the normal spectrum of human weirdness. It's unclear to me that the stranger elements of his Mormon background would have an effect on his decision making as a president. It reminds me of how many were afraid of JFK's catholicism in the early 60s. Romney makes no connection between his political positions and the eccentricities of Mormonism.
The situation is quite different with someone like Michelle Bachmann, who explicitly indicates that her ideology is the central factor in her political positions. Her ideas are a predictor of her decision making behavior because she so specifically connects her ideas with her intended decisions. I personally think it is better for a president to be a pragmatist with good overall goals and a good working knowledge of how things work than to be an idealist.
This is not an endorsement of Romney. I'm simply trying to present some perspectives that I find somewhat lacking right now among evangelicals in the public forum.