I’m agnostic about where he was born, but boy do I have suspicions! Even, as you say, even if it’s not his birthplace, there’s something special being hidden. Your idea, though, about the BC having Muslim - while it might be right, they do have that Indonesian school paperwork already which says Muslim and Indonesian citizenship. Unless maybe by it’s being on a BC it might carry more weight. I don’t think my BC says what our religion was - although back then, you usually gave birth in a religious hospital, which kind of gives it away!
My brother and I, and his two kids, were born in a Catholic hospital. None of us are Catholic, although my father was at one time. (He went to Catholic school, but got kicked out, the last straw was eating raw onions, as one would eat an apple, in class :) )