I have absolutely nothing against Mormons. I'm not one of the 17 percent.
But the way that JFK won in 1960 was by distancing himself from the Pope.
A Mormon cannot distance himself from his/her prophet. And Americans don't like the idea of someone running the scenes from backstage.
Of course they can. Romney certainly has. Just one example: the LDS Church is the fiercest defender of the Boy Scouts from the infiltration of gay activism. Romney stated very publicly that he was of a different mindset.
Now, it is true that LDS members who are social liberals tend to fall into inactivity with respect to their church affiliation. There is no shortage of such LDS members in Utah. Salt Lake mayor Rocky Anderson is a prime example.