As someone who knows the Prince personally, I am certain he’s no Moslem.
I’m not entirely sure he’s truly a Christian either which is of concern given his future role as Supreme Governor of the Church of England (although of no personal concern to me, as I’m only nominally a member of the Anglican Church myself nowadays) but he hasn’t joined any other faith.
The idea that he has seems to me to have come about because of his publically expressed desire to be a ‘Defender of Faith’ - I believe that desire stems from nothing more dramatic than a belief that he wants to be a King for all his people. He has a sense of duty that is quite inspirational.
I believe we wanted that changed to "Defender of the Faiths," which brings up the whole issue.