(1) to say that subscribing to Islam would not be an issue is disingenuous
it was under the banner of Islam that an attack was launched on 11 September
it was Muslims world-wide (including here in the USA) that celebrated the event
it was Muslims here in the USA that so admired the event they attempted to stage events similar to that event
published studies of (mostly black) converts to Islam here in the USA convert to Islam, not because of theological concordance, but because of the anti-American aspect of the exponents of that ideology)
(2) By no means is it the same God they worship as the God of Christianity
as Rilke might put it, the way you use your God makes him a different God than the way I use mine
the God of Christianity was formed over thousands of years as his worshipers prayed first for their material safety and well-being, and then questioned what was the right thing to do ... over generations, theses considerations were collected, written, and discussed, then with further soul-searching compiled as "the Word"
Islam arrived after all this, and found it's genesis in a sect that sought to break away from the larger Jewish society and hierarchy ... so, from the beginning, sought to distinguish itself from the larger group, demonizing the larger group as part of the rationale for the division ... to support and authenticate the division, they concocted the prophet Mohammed ... so unlike Judaism, or Christianity, the basic thrust is ant-Judaism ... as can be seen from the teachings that have been the object of many communications from the USA State Department to Riyadh ... many times the USA has had to advise Riyadh to stop the anti-Jewish rhetoric
(3) the question of whether Obama is or is not Muslim, is thus relevant, but probably moot