My father-in-law is of the opinion that the president is a Muslim, and facts to the contrary don't budge him. He did have a ethnically-Muslim father and did spend some of his formative years in Indonesia, but only if you consider that a lineage thing would that be the case.
One of the reasons for that logical glitch is that Obama's policies have erred on the side of Muslim countries and against Israel and "Christians." That can be better explained from having a secular anthropologist mom than an absentee atheist of Muslim stock dad.
Israel is seen as a colonial power by modern leftists, so they reflexively side with the Muslim countries in the area, even though Israel is far more accommodating of secular liberals than their Islamic foes. The BSD folks on the left have far more left-listing Christians than Muslims.
The Arab Spring had Obama siding with Salafis in Egypt, but that could be seem as a pro-democracy move, one that a Republican would well have agreed with. Sadly, the Egyptian military didn't give their Muslim Brotherhood folks a chance to show if you could have a civilized Islamic government.
Obama seems to be a liberal Christian; the right side of the Peanut Gallery might question whether a well-left UCC can be called Christian, but that's how he says he rolls. If he's a closeted Muslim, he's hid it VERY well.
Thus, when we get a questioner at a NH Trump town hall both playing the birther card and the Obama-is-a-Muslim card; Trump's failure to call BS is high on the news today. The questioner seems so much a stereotype of a birther such that folks think he might have been a plant to make Trump look bad.
Trump was late to the birther party, but he hit the ground running with a flourish four years ago when he played with a presidential run. He opted not to run then, but that might have started to burnish his credentials as a reactionary, playing to a non-trivial chunk of the GOP who assume that he's too foreign to be president and too foreign (to their worldview) to be an American.
One could make a good case that Obama is as much of a Christian as Trump is, and possibly even more so. Obama at least makes a run at bringing home a social-gospel help for the little guy, while Trump brings this CCM oldie that I finally tracked down yesterday (I wore out my Watercolor Ponies cassette two decades ago) to mind.
Materialism does have a spell on The Donald, among other things.