You forgot to mention  the Deists along with the Masons. Or the fact that the Christian bloc amongst the founding fathers wanted Washington to take the crown as King George I (keeping in mind that the Christian church in question was adherents of the Church of England, or schismatics like the Pilgrims who thought the church to liberal). Or make their religion a legal constitutional requirement....although there would be unspoken 'tolerance' winkwinknudgenudge for other faiths.

And yeah, it is rather apalling at how much subjective wish fulfillment gets spouted as fact. Although it can be highly satisfying if you can get a dogmatic to stop and actually think for a minute.