What is interesting is that they understood that they needed to leave religion out of state affairs. This was the equal and opposite reaction to figureheads like Henry taking over a new Church and setting himself as it's divine leader. It wasn't that the people at the convention weren't God fearing... hell, Jefferson rewrote his own bible... but they wanted the freedom to believe what they believed and the right for others to do the same. That was unique in history. No other government has really adopted such a view. Rome was inclusive. Greece was inclusive but they appropriated those other religions as extensions of their own and used that as a justification for their right to rule.
Catholicism derived it's authority by intertwining with the Empire and well... that experiment seemed to work for a very long time, didn't it? However, it didn't allow for the freedom of expression that made Christianity so appealing in the first place. That's why centuries later, you have figures like Calvin and Martin Luther able to capture the angst of all these disparate groups and start a reformation. There wasn't one monolithic idea against Catholicism, as always, each group had their own concerns, their own Godly needs. What religion offered was a way for the individual to matter to the whole. When that religion failed to fulfill that need, the individuals broke that system.
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