It would depend on the Muslim.
Consider first a parallel question: Could I support a Christian for president? Yes, other things being equal, but not if he or she is a theocrat. Why not? Because theocracy is incompatible with the principles, values, and founding documents of the United States of America.
Similarly, I could easily support a Muslim such as Zuhdi Jasser for president (were he to run) because he is not a theocrat or a supporter of Sharia. To be precise: Jasser's being a Muslim would not count for me as a reason not to support him, even though I might have other reasons not to support him, for example, unelectability.
When Dr. Ben Carson said he could not support a Muslim for president what he meant was that he could not support a Muslim who advocated Sharia. That was clear to the charitable among us right from the outset. But he later clarified his remarks so that even the uncharitable could not fail to understand him.
Some dismissed this clarification as 'backtracking.' To 'backtrack,' however, is to say something different from what one originally said. Carson did not 'backtrack'; he clarified his original meaning.
Nevertheless, CAIR has absurdly demanded that Carson withdraw from the presidential race.
Is there anything here for reasonable people to discuss? No. Then why is this story still in the news? Because as a nation we are losing our collective mind.
It's like Ferguson. What's to discuss? Nothing. We know the facts of the case. Michael Brown was not gunned down by a racist cop seeking to commit murder under the cover of law. Brown brought about his own demise. On the night of his death he stole from a convenience store, assaulted the proprietor, refused to obey a legitimate command from police officer Darren Wilson, but instead tried to wrest the officer's weapon from him. He acted immorally, illegally, and very imprudently. He alone is responsible for his death.
So there is nothing here for reasonable and morally decent people to discuss. But we are forced to discuss it because of the lies told about Ferguson by the Left. The truth does not matter to leftists; what matters is the 'empowering' narrative. A narrative is a story, and a story needn't be true to be a good story, an 'empowering' story, a story useful for the promotion of the Left's destructive agenda.
Another pseudo-issue that deserves no discussion except to combat the lies and distortions of the Left: photo ID at polling places.
Exercise for the reader: find more examples.