"Would anyone be agreeable with not electing a quietly practicing muslim "in case" they tried to impose sharia law?"?
Yes I'd say without any doubt that most, maybe not all, conservatives would not be agreeable to electing a muslim at all. Just read the conservative commenters on G&M. 
Anf if the muslim got to be leader mostly because of votes from people who now expect him to promote shariah law, so he is beholden to them,  then I'd be against him too. And that's very close to the case here.
BTW, I'd say electing a muslim wouldn't worry me at all. But, just like everybody else here, I'm just an anonymous poster. So no real point in asking that type of question.