This is at base incorrect. The problem they saw was the mix of government and religion. They wanted religion free of government and government free of religion because of the corrupting power each had on the other. Saying they were deists is technically correct while ignoring the change in context of that word in time. Deism back then was a hell of a lot more religious than it would be considered now. What we now consider religious persecution they likely would have seen as maintaining basic community standards.This is correct. Religion was considered tyranny by the founders of this country. That was one of the main reasons for breaking away from England. They believed no one should be persecuted for their beliefs.
And they wanted it kept free from the federal government. Several state churches were already established at the time of ratification and no one saw that as incompatible with the constitution. Then as now, immgration patterns held and like minded people tended to stick together, states were very homogenous when it came to their religion. As such... "I consider the government of the United States as interdicted by the Constitution from intermeddling with religious institutions, their doctrines, discipline, or exercises. This results not only from the provision that no law shall be made respecting the establishment or free exercise of religion, but from that also which reserves to the states the powers not delegated to the United States. Certainly, no power to prescribe any religious exercise or to assume authority in religious discipline has been delegated to the General Government. It must then rest with the states, as far as it can be in any human authority." --Thomas Jefferson