The founding fathers were a complex and varied group. It's perhaps most true to say that there was no common baseline for either familiarity or opinion in regards to non-Christian religions - both varied based on the founding father. To start though, let's discuss the founding father best known to be related to this topic: Thomas Jefferson, and the non-Christian religion he's best associated with: Islam.

Jefferson bought a Quran at the age of 22, while he was still a law student. In early political debates he lumped Islam in with Catholicism claiming they "Stifling free inquiry." Regardless in private notes he kept he wrote “Neither Pagan nor Mahometan [Muslim] nor Jew ought to be excluded from the civil rights of the commonwealth because of his religion.” This suggests that Jefferson both harbored a personal prejudice against Islam, and believed it should nonetheless be protected under written law. Islam was certainly not unknown among the founding fathers. Many slaves were adherents to the religion. But apart from Jefferson, I do not know of any evidence that other founding fathers had a more intimate knowledge of the religion other than basic awareness.

In terms of Judaism, John Adams wrote in favor of a Jewish return to the holy lands, stating that a return would: “wear away some of the asperities and peculiarities of their character and possibly in time [they could] become liberal Unitarian Christians.” Jefferson wrote that Jesus "exposed their [The Jews] futility and insignificance" in a letter to William Short.

The majority of the founders were Protestants. Distrust of both Catholics, and of other Abraham religions like Judaism and Islam was common. Familiarity was basic at best, Jefferson was the only founding father of importance to have read a holy book other than the Bible, for example.

To to answer your question in the simplest terms. You would be familiar with both Judaism and Islam. You may have a pastor or preacher who has spoken on the subject. Your personal views would run the gamut from non-interest to personal prejudice. But you would nonetheless support their freedom of religion.

I cannot find evidence that any founding father was directly familiar with a non-Abrahamic religion like Buddhism or Hinduism. If there is information on that topic, I was not able to find it.