They were Christian, and the major religious groups were Protestant, Puritan, and Quaker.
Seeing as our Founding Fathers were "Christians", I would guess that they believed in a more methodist or puritan (Amish?) style of Christianity than I or any other Christian does today.
And no, they most certainly did not follow Mormonism, as they did not exist before the pilgrims, and Buddhism isn't an option either.
Also, the reason why the Bible was able to be taken out of schools was that there were so many unwritten rules in their time, that so many things were assumed that they had no need to actually state what everyone really believed. In their day, the possibility of our nation going the way of Sodom and Gomorrah was just not possible to them. And now, we have middle-school kids on birth control and pedophiles a plenty! Hooray America!