Jefferson may have had some clue, but only after becoming President and having to deal with the Barbary Pirates.
Adams and Washington also knew about the Barbary Coast Pirates and in fact 15% of the revenue of the nwe USA was to pay these pirates for unfettered passage. The new USA was very pacifistic and it was thought that 15% was to avoid war. But that pacifism did not last as more was demanded by the pirates. Jefferson was forced to send the Navy to battle the pirates.
Posts 15 and 21 I believe more accurately cover the real reasoning the Founders had in ignoring Islam.
But I still think the Founders had no idea that Islam is a cult or religion that cannot be made by the force of law to coexist with other belief systems. The reason we see them now in apparent coexistence is because their numbers are small. As soon as they grow large enough, we will see them emerge to change law favoring their religious beliefs and squelching all others.
The Muslem creed is one where if anyone says anything that is disrespectful to their religion, the adherents take it as a personal insult to their prophet/god Mohammed and they are ‘hurt’ by such criticisms. Hurt always leads to anger and anger uncontrolled leads to violence. The only way to calm Muslims is to submit to their doctrine. They are a cult of conquering anything and everything that is not Muslem. There is no way for them to coexist over the long term with any others.
Whereas Christians take criticism everyday and acknowledge they are sinners who must nevertheless try to understand and repent of their condition that they can do nothing about. Christians are left to defending, never offending although history has counterexamples.
I just don’t think the early Founders knew what it must be like to have Muslims in great numbers living next to them. They knew of their piracy and deceit and crazy beliefs, but not the steady encroachment and uncompromising cultural transformations that Muslims today never stop pushing for and can’t stop pushing for. There is one example in history that I know of where my statement doesn’t seem to fit, and that is the history of Ataturk in Turkey.