I don’t know about you, but I would have a hard time voting for a Muslim, especially during these times.
We have probably had atheist and agnostic presidents, but they didn’t admit it and pretended to be Christians because they knew the electorate would never vote for an unbeliever. Of course, some of our presidents during the early republic may have been Deists.
It is true the US constitution prohibits a legal religious test for office, but that does not extend to the electorate. Any of us are free to vote on any basis we want, including religion, race, hair or eye color, or anything else.
Once, years ago, my mother and I were watching a political commercial on TV. I made a comment about the candidate, and she said, “I could never vote for him. Thin lips.”
The problem with Romney’s theology is that it reveals a strongly supersessionist bent - newer, better ideas replace the outdated. This, as well as his political history, would suggest that he would be very comfortable with a loose constructionist view of the Constitution.