Do you think Chuckles the clown is a Muslim or not??
Definitely not. Besides anything else, I've seen him eat bacon at breakfast - and for that matter, the company associated with the Duchy of Cornwall - his company, in essence - manufactures and sells bacon, ham, and pork sausages.
He's not Muslim - he's a Christian and a member of the Church of England, and I would say he's somewhat more Christian than the the modern Church of England requires somebody to be, although that's not necessarily saying much.
He treats Islam with respect, just as he treats Judaism with respect, Hinduism with respect, Buddhism with respect, etc, but it's only with Islam that this seems to be controversial. He does not treat those who use their religion - any religion - as an excuse for violence - with any respect at all. He believes terrorists should face the full weight of the law, but he makes a distinction between terrorists who claim a religious justification, and ordinary people who just want to live their lives following a faith that they may have been born into. In understanding his position, I think it's important to remember that throughout his lifetime, terrorists who claimed their terrorism was linked to Roman Catholicism, have repeatedly set off bombs all over his country, as well as assassinating the man he was closest to outside of his own direct family, the man who mentored him through his adolescence and young adulthood. He makes a distinction between those who will use a religion to justify crimes and terror, and those who just want to live a religious life. He has no time for Islamist terror - besides anything else, as he knows his entire family make spectacular terrorist targets for somebody who wants to make a point, he's far more acutely aware of terrorism than I think most people are.
The Prince is not at all like the caricature presented of him in the Press. He's a conservative on most issues (environmentalism is an exception, but even there, he's nowhere near as extreme as he's presented - as in this case, speeches are often not actually reported, and a lot of the time it's not made clear that a speech may have been largely written for him by the government (it depends on the topic - he doesn't write his own speeches - although he generally does write articles that appear under his name - but sometimes he has a lot of influence on the speech, and sometimes he doesn't - constitutionally, he has to be very careful not to publically criticise government policy). He's not a perfect man by any means - despite his position, he is, of course, as flawed as any other person might be - but he's a good and decent man trying to do his duty to his country and the Commonwealth, and mostly doing it well. As his friend, I don't like the way people have been made to see him, much. He shrugs it off himself, but he doesn't have much choice.
He certainly is not Muslim.