No, I wouldn't vote for anyone who believes it's okay for politics to be influenced by religion - and muslims do this to the greatest extent.
No; the cultural differences are too great. I am qualified to say so as I have lived and worked in the middle east and I married into a Muslim family.
If any candidate agrees that the government should not participate in the establishment of religion, favor one religion over another, and should allow people to freely exercise their religious beliefs without impeding the rights of others, I would be willing to vote for them if I felt their policies were best for our country.
If a candidate did not have these attitudes toward religion, I would probably not vote for them.
Long ago, we decided that neither a theocracy nor a state-sponsored religion was the way to go. That was a step in the right direction.
You're supposed to keep religion for yourself (that's secularism). So I wouldn't mind because he/she is supposed to keep any form of religion for him/herself.
Muslims are humans. None has the right to alienate them on the basis of a religious identity. People are sensible or ignorant irrespective of their identities. it doesn't matter whether the person is muslim or hindu or christian or woman or gay.