There were many spicy quotes during the Enlightenment -- the founding fathers were reflecting a common sentiment among the educated classes in Europe. Anyone interested in that time period would enjoy Peter Gay's book about it. It's incredibly well-written and much less dry than a book about that subject has any right to be.

One can be part of the system and recognize its faults.

Yeah, there were some people sort of bucking the system, and probably some closeted atheists, but criticizing the church for its corruption and failures is no different than us doing the same about our government today.

The next line after the quote is:

Upon this system depends The Royalty, Loyalty, and Allegiance of Europe. The Phyal of holy Oyl, with which the Kings of France and England are anointed, is one of the most Splendid and important Events in all the Legends.

So not necessarily an anti-deity statement, but more an acknowledgement that the Church is a system by which European rulers reinforce their power and wealth. The whole letter to Taylor from Adams really rants about the church’s power and attempts to control people’s lives.

If the scriptures had been written with one half of the care and ability with which they have been explained and defended, they would not have been the cause of so much contention and mischief, and they would not have stood in need of so much explanation and defense.

and

To suppose that God Almighty has confined his goodness to this world, to the exclusion of all others, is much similar to the idle fancies of some individuals in this world, that they, and those of their communion or faith, are the favorites of heaven exclusively; but these are narrow and bigoted conceptions, which are degrading to a rational nature, and utterly unworthy of God, of whom we should form the most exalted ideas.

and

The discoveries of science have proved that the opinions concerning a firmament above, and a flat earth beneath, are completely inaccurate; but faith delights more in sublimity than truth; it soars far above science in its discoveries, and holds accuracy in contempt.

and

In those parts of the world where learning and science has prevailed, miracles have ceased; but in such parts of it as are barbarous and ignorant, miracles are still in vogue; which is of itself a strong presumption that in the infancy of letters, learning and science, or in the world's non-age, those who confided in miracles, as a proof of the divine mission of the first promulgators of revelation, were imposed upon by fictitious appearances instead of miracles.

--Ethan Allen, Reason: The Only Oracle of Man

Payne was a proto anarchist. His response to coming to America was “this no king thing is awesome but let’s look at the Haudenosaunee Confederacy and maybe since we’re on their land consider that they might be living better lives than us.

who was as close to an overt atheist as you could get in the 18th century without having someone come up behind you and slit your throat.

I don't really think that was a risk. My understanding is it was more like: "well this is what smart people have believed for centuries- what idea do you have for where we came from?"