Knew that they couldn't have both religious and secular influences
Let's take from Jefferson an example of his open mindedness regarding rational thought (empiricism) and religious morality:
"The truth is that the greatest enemies to the doctrines of Jesus are those calling themselves the expositors of them, who have perverted them for the structure of a system of fancy absolutely incomprehensible, and without any foundation in his genuine words. And the day will come when the mystical generation of Jesus, by the supreme being as his father in the womb of a virgin will be classed with the fable of the generation of Minerva in the brain of Jupiter. But we may hope that the dawn of reason and freedom of thought in these United States will do away with all this artificial scaffolding, and restore to us the primitive and genuine doctrines of this the most venerated reformer of human errors."
-letter to Adams, 11 April 1823
"But enough of criticism: let me turn to your puzzling letter of May 12. on matter, spirit, motion etc. It's croud of scepticisms kept me from sleep. I read it, and laid it down: read it, and laid it down, again and again: and to give rest to my mind, I was obliged to recur ultimately to my habitual anodyne, 'I feel: therefore I exist.' I feel bodies which are not myself: there are other existences then. I call them
matter. I feel them changing place. This gives me
motion. Where there is an absence of matter, I call it
void, or
nothing, or
immaterial space. On the basis of sensation, of matter and motion, we may erect the fabric of all the certainties we can have or need. I can conceive
thought to be an action of a particular organisation of matter, formed for that purpose by it's creator, as well as that
attraction in an action of matter, or
magnetism of loadstone. When he who denies to the Creator the power of endowing matter with the mode of action called
thinking shall shew how he could endow the Sun with the mode of action called
attraction, which reins the planets in the tract of their orbits, or how an absence of matter can have a will, and, by that will, putt matter into motion, then the materialist may be lawfully required to explain the process by which matter exercises the faculty of thinking. When once we quit the basis of sensation, all is in the wind. To talk of
immaterial existences is to talk of
nothings. To say that the human soul, angels, god, are immaterial, is to say they are
nothings, or that there is no god, angels, no soul. I cannot reason otherwise: but I believe I am supported in my creed of materialism by Locke, Tracy, and Stewart. At what age of the Christian church this heresy of
immaterialism, this masked atheism, crept in, I do not know. But a heresy it certainly is. Jesus taught nothing of it. He told us indeed that ‘God is a spirit,’ but he has not defined what a spirit is, nor said that it is not
matter. And the antient fathers generally, if not universally, held it to be matter: light and thin indeed, an etherial gas; but still matter. Origin says ‘Deus reapse corporalis est; sed graviorum tantum corporum ratione, incorporeus.’ Tertullian ‘quid enim deus nisi corpus?’ and again ‘quis negabit deum esse corpus? Etsi deus spiritus, spiritus etiam corpus est, sui generis, in sua effigie.’ St. Justin Martyr ‘to theion phamen einai asomaton, ouk hoti asomaton, --epeide de to me krateisthai hupo tinos, tou krateisthai timioteron esti, dia touto kaloumen auton asomaton.’ And St. Macarius, speaking of angels says ‘quamvis enim subtilia sint, tamen in substantia, forma et figura, secundum tenuitatem naturae eorum, corpora sunt tenuia.’ And St. Austin, St. Basil, Lactantius, Tatian, Athenagoras and others, with whose writings I pretend not a familiarity, are said by those who are, to deliver the same doctrine. Turn to your Ocellus d’Argens 97.105. and to his Timaeus 17. for these quotations. In England these Immaterialists might have been burnt until the 29. Car. 2. when the writ de haeretico comburendo was abolished: and here until the revolution, that statute not having extended to us. All heresies being now done away with us, these schismatists are merely atheists, differing from the material Atheist only in their belief that ‘nothing made something,’ and from the material deist who believes that matter alone can operate on matter.
Rejecting all organs of information but my senses, I rid myself of the Pyrrhonisms with which an indulgence in speculations hyperphysical and antiphysical so uselessly occupy and disquiet the mind. A single sense may indeed by sometimes deceived, but rarely: and never all our senses together, with their faculty of reasoning. They evidence realities; and there are enough of these for all the purposes of life, without plunging into the fathomless abyss of dreams and phantoms. I am satisfied, and sufficiently occupied with the things which are, without tormenting or troubling myself about those which may indeed be, but of which I have no evidence.” –letter to Adams, 15 August 1820, his italics
I could go on; but that’s a lot of typing already. You should read this for yourself. Suffice to say: Jefferson (and Adams and other Founders) was buried deep in a wide variety of non-Christian philosophies, and our country was founded with a complex of many, not just “Judaism/Christian” principles.
, we must start with the epic of gilgamish, move into the vedas and so forth... 
