In all fairness - the accusations are not simply that he is a Muslim, but that he has been lying about his faith in order to subvert criticism of his Muslim faith. That would be a major concern if the rumors were true.
Other than that, any faith that is outside of the US mainstream brings deeply held beliefs that might be hard for large swathes of society to accept. The more exotic, the more different ideals, the more people will question them.
Look at what they did to Romney over his faith.
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