I gave a tentative yes. My hesitance is unrelated to the Muslim thing. It's more along the lines of Objective-J's apprehension.
Why announce right before the election? What's with the sudden conversion? "Oh my god" moments (no pun intended) during times of extremely high stress (like an election) make me a bit nervous about the stability of the candidate, regardless of what their "oh my god" moment is.
The fact that they're Muslim wouldn't matter. The situation surrounding it would.
But for the purpose of this hypothetical, I am going to assume that nothing about them has changed except their religion. In that case, yes.