I question the wisdom of even having this sort of argument. Whatever the founders intended, we have a system of laws that isn't based on their intentions except through a long chain of history. Divining their intentions and pretending they're still pertinent is akin to saying that "xenophobia" means "fear of outsiders" and cannot include "hatred of outsiders", because "phobos" meant "fear" to the Greeks. This sort of etymological argument sheds no light except on... well, etymology.

There are no such things as religious nations or rational nations or <fill in the blank> nations. There are groups of people with founding documents that may have religious or rational flavors, there are perhaps ideologies that are at least nominally shared by all a nation's inhabitants, etc.

... but there is no binary switch which is set at the founding that determines whether a nation is rational or religious. There is no soul, individual or national, and there are no essences, either of individuals or nations. It doesn't matter where we came from - these are the laws currently on the book and we should debate their current interpretation and merit, not their origin. There aren't kinds of nations - there are nations situated squarely in their historical and present contexts, with their historical legal canons and current interpretations.

It's a red herring argument. The founders are dead and with them, their authority. Does the current interpretation of the law permit favoritism by the government for certain faith groups? Do you want it to? Do you want it not to? Are you willing to work within the current system to bring that about or do you want to burn everything down? At no point do we need to perform necromancy to figure out some dead man's interpretation - at the very worst we can look back a few decades to a more recent legal ruling.

It's like saying "yes, perhaps this is the way 'phobos' was used in the past, but in current usage..." This is a much richer conversation to have.