I have been unable to find any information about John Randolph being a Muslim. He was renowned as an eccentric, so it wouldn't have been overly shocking.
Maybe somewhere in the writings of Francis Scott Keyes. It could be true, I'd just like to see further confirmation.
I have a copy of the 11th edition of the Encyclopedia Britannica on my shelves, and just checked that that quotation I found on the internet is accurate.
I have The Education of Henry Adams, but I don't have his biography of Randoph at hand. His reputation was that he was an eccentric and an extreme Deist, I think, which is to say probably an agnostic or an atheist.