I’m with you.
I think the possibilities range from: (1) his birth certificate, a legitimate one, cites his religion as Muslim because BHO Sr stated as much on the long-form BC; or (2) his mother relinquished his natural-born citizenship for him when he was adopted by his Indonesian stepfather. This explains why some recall him attending Occidental College as an international student.
One of his law partners wrote a long law review article back in 2004, just after his election to the US Senate and discovery by George Soros, in which the “natural birth” req’t of the Constitution was decried as being worthy of change.
It’s the tiny bits of evidence that are sometimes most revealing.
HI birth certificates do not list a child’s religion; I don’t think any do.
1961 Hawaiian long form birth certificates have no field for "religion", nor does any other US one I've seen.
By US law, a parent cannot forefite the citizenship of a child. Nor can the child renounce it themselves, until they reach a more mature age, generally 18, but in some cases younger if they can convince a US consol that they are not being influenced or pressured by anyone to renounce their US citizenhip. And the bar for that is very high.
I have never seen a birth certificate that states religion.
I don’t think state birth certificates require the religion of the parents to be listed. My wife and mine for Indiana, my daughters for Maryland have no listing of ‘parents religion’. Thus I don’t think you fixation on “muslim” being on the birth certificate is reasonable.