I believe the Founding Fathers were generally affected by two things:

1) The religious strife in Europe and the Middle East (Reformation and Crusades) which killed many and hindered larger cooperation.

2) The Age of Enlightenment, which beget things like Science and Freemasonry (which peddles a kind of transcendent and generic God who can span multiple religions). Franklin and Washington were both prominent Freemasons and a large influence on our Constitution.

You're right that most at the time were Christian Protestants, but there was also a strong sense that a church-influenced government was a vector for corruption (and vice-versa), Franklin knew the value of Christianity, but also knew its flaws and the need for transcendent statehood.

It all worked out well for us, where else do you have so many diverse (and weird) religions (Mormons, Amish, Jews, Sikhs, Catholics, Evangelical Protestants, etc) that largely cooperate effectively in business and war under the broad banner of free will, democracy, and capitalism? Problems arise for sure, but a largely self-correcting system.