It is basically like a cover. I don't know if they directly said they were deists or if people later referred to them as that, but the definition of that is like you believe in other gods or entities, just not the poop jew one. The only ones really left at that point are the Pagan gods.
Follow that up with all the Satanic symbolism in the architecture and money and in the legal system, and it sort of fills in the blanks for you.