You are missing my point. Which is: Even Deists embrace the idea of the Creator God, Who endues all created things with an inviolable, inalienable nature (which the State is forbidden to transgress).
Jefferson — that marvelous "American sphynx" — was almost certainly a Deist. The same is alleged of Franklin. So what??? Both embraced the Creator God which at the very least we can say is an Old Testament concept.
The fact is all the Framers were wholly enculturated into the Judeo-Christian tradition. This despite they were all highly educated men, mainly classically trained, and children of the Enlightenment. Many Christian denominations (except it seems Catholic) were represented in their ranks.
But they did not want in any way to establish a theocracy: No State preference should ever be given to any particular religious denomination, including their own. The language "Our Lord, Jesus Christ" as a modifier of "the Creator" would have offended against the very principle of freedom of religion that they were trying to establish, by seeming to favor one particular type of religious belief over all others.
But to say that the government should not favor any particular religion is not the same as saying that the government should be hostile to religion. Particularly in the case where frankly religious ideas stand at the very foundation of our system of individual liberty under equal laws and justice.
The Old Testament mythology has its god as an over-dramatic individual, DIRECTLY interfering in human affairs.
Deism is the polar opposite of such a concept- in that its main ideology is that there is no such interference- a mere stepping stone to formal Atheism.
One of the distinctions the article misses is the difference between the general period of the enlightenment (which helped spawn classical liberal thought in the old Whigs) and that step child imitation, the French Enlightenment.
Gertrude Himmelfarb does a good job of distinquishing between the three enlightement traditions pointing out the English-Scotish enlightenment which held religion essential to the fostering of moral men was so successful at creating real liberty and prosperous civil society that two other traditions sprange from it with end-goals to improve it but still achieve its benefits.
The first was empirical and took place in America using empirical elements of what worked in the American setting. The second imitation failed as the French, followed by others later, rejected empirical tests and substituted rationalism and metaphysical concepts all stated out with rigid logical constructs.
Hayek agrees in The Constitution of Liberty and spells out that distinction clearly in chapter four.
We can’t seperate all the history while claiming to reference it as this author does.
Some tradition. TJ thought Jesus was an illegitimate child and NOT the Son of God!