I think what I write next needs to be stressed in the study of George Washington's personal religious beliefs.
After reading virtually everything George Washington said and wrote on religion, I conclude GW believed in an active personal Providence.
However, Washington was also imbibed in Greco-Romanism, particularly Stoicism. I'm still trying to get a handle on what the Ancient Greek and Roman philosophers -- the ones who didn't believe in mythology (Zeus, Hercules, etc.) -- believed religiously. As far as I can tell, they believed in some kind of impersonal deistic-Providence.
Again, Washington (of all the Founders, especially) drank deeply from that well. So we see quotations where GW refers to Providence in an impersonal sense, calling Providence "It" and "She" at times, sounding like a deist. (You'll have to trust me he did this; I'll provide the quotations elsewhere if requested.) I think he was being sincere when talking about Providence this way. He was just sounding like the neo-Stoic he was.
However, elsewhere (over and over again) he refers to Providence as an active personal God, and seemed to believe in a warm universal theism.
If one focused only on those letters where GW invoked the neo-Stoic impersonal Providence I understand why one would (inaptly in my opinion) conclude him a "deist." (You still have to put his impersonal Providence talk together with his warm theism talk.)