Well, not long after it was ratified, there was a strong move to re-edit the preamble to the Constitution, worded in such a way that only protestant-christians would qualify as citizen, catholics, jews, ect, need not apply.<quoted text>
Can't quite agree with the "far more of the founding authors of the Constitution would've come out as full-on atheist" there. Prior to the US, the colonies did have state sponsored religions.
Maryland was Catholic, Pennsylvania was Quaker, Massachusetts was Puritan, Rhode Island was a splinter group from Massachusetts. Virginia was Baptist. and so on.
So yes, the founding of the US was primarily by Christians, but the freedom of religion clause was thrown in there because none of them would agree to which flavor should be the national religion lest their particular brand not be the dominant one.
In a way, you could say it was a cinematic version of a Mexican stand-off. Whoever shot first to take dominance would surely die.
It was strongly rejected, though-- the effort being led by Jefferson (as I recall). The new wording would have included the words "jesus christ" among other pure-christian idiocy.
That says to me, that Jefferson and the others were more interested in keeping it secular, not religious.
So I think I was correct: had it not been politically suicidal to be full-on atheist, I suspect many would have been.
Then there is the habit of culture, which had a strong influence too.