THAT is crucial; in Western tradition, even the notion of the "Divine right of Kings" had a corollary right out of the Old Testament: the King was either a good king or a bad king insofar as he followed the laws given by God.
Ethan Allen and Thomas Paine were deists and said so. Two or three minor figures were also deists. The rest were Christians. Heretical Christians often because some-- Jefferson and Franklin for instance--did not subscribe to the Nicene Creed, but Christians none the less.
The left has been on a crusade for some time to inculcate the idea into everyone's skull that America was not founded by Christians. That is why the "deist" label has been slapped on them.