It is real history, but the inferences that you draw are not necessarily correct.
Since the other side in question was Muslim in practice, and since most countries in Europe and now this very new republic Were said to have or to be considering some sort of state-sanctioned religion, the phrasing of the article was felt to reflect a reassurance to the Pasha that there would be no ‘religious wars’ and no attempt to engage in such. It was not meant to stand as an ‘11th commandment’ if you will. Perhaps you believe so much in ‘separation of church and state’ that your worldview necessarily causes you to read everything ‘in that light’ and to view the wording and phrases of a document written in 1797 as by men who had the outlook of early 21st century men. That is not the case at all.
Also, the whole “most of them were Deists’ is a kind of revisionist ‘wish’; while many of those involved in the early stages of the U.S. were interested in the “Enlightenment” and members of the Masons etc., they were also men, men who lived in a particular era, men who participated in something, well, revolutionary. I am reminded of men who are wildly enthusiastic about something, be it “Dungeons and Dragons’ or perhaps going to ‘radical meetings’ in their youth, who after a few years begin to find themselves interested in things that are quite different.
Or to be somewhat historical, and as somebody whose older sister was a perfect flower child, the ‘peace and love’ age of Aquarius 20 year old in 1968 was pretty quickly the cunning 40 year old Wall Street trader in 1988, for example. My goodness, the commune-loving, back to the land, simple living 20 year old who wanted to bake bread and smoke tokes was the person who wanted to get rich quick, ‘the one who dies with the most toys wins’, and snorting coke.
What I mean is, and considering times and pursuits, for rich and poor alike were more more homogenous and simple then, the 20 somethings who were taking over in 1800 from the 50 somethings who had actually fought as young men themselves in the war and just prior, would themselves in another 20 years be going right into the Great Revival (look it up).
And even the Founders had a lot more on their plate—and in their worldview, which lacked diversions like the internet—even than discussing “Deist’ principles. There was also a lot about personal wealth to consider, and manifest destiny, not to mention an eye for industry. Such things would be of far greater import than a desire not to have a ‘state sponsored religion’.