My impression was that original constitution was inspired in some way by John Locke but I might be mistaken.
[This balanced approach was not taken by later colonies that left out all religious obligation. That does not seem right to me. Perhaps they thought the trouble was in the churches themselves with lots of problematic doctrines. And that problem has not seem to have been abated. I guess they could have chosen the best ones, and forbade the less desirable ones;--but instead they choose to say that Federal government ought to stay out of religion altogether. Anyway, I think some of the Founding Fathers were Deists anyhow, so it would not have made any sense to have clause that one has to belong to some church. Instead they focused on the mechanisms of government and tried to get that part right. That seems to work well. In that way they left the power to the states to support whatever religious orders they saw fit- and that seems to have worked well until recently. Even the Mir yeshiva in NY I think was getting state funds for being a institution of higher learning. So this approach of the founding fathers seems to be a pretty decent model of government.