These days? certainly. This is the party which has a wing that accuses conservative activist Grover Norquist of being a secret Muslim. If circumcision weren't the norm among American men, I'd bet they demand he drop trou. Not only does the base employ religious tests, it employs insane religious tests.

It would be interesting to see how a modern Mo Udall would perform generally. Mormons aren't a monolith, and most of them have traditional mainline Protestant values. They do feel culturally embattled, though, and the Republican Party caters to that.