How you posited this is generally true, but let's also not forget that the FF were speaking of a very specific religious instruction at that---a Protestant one. Not a Christian one, per se, because Christianity also includes Catholicism, of course, and I'm sure you know that John Adams and other third- or fourth-generation Massachusetts Puritans of the era didn't exactly fawn over papists. As a matter of fact, New Englanders were more than happy to commit ethnic cleansing against the "evil" French Neutrals in Nova Scotia---l'Acadie. I'm sure those good Congregationalists were sure they were being morally upstanding by destroying the entire Acadian culture and scattering their remnants to the winds, but that explanation was only window dressing. Their real interest was seizing their territory and re-settling the prosperous Acadian farms with good, loyal Protestants.
And then again, there were the spittin' mad differences between the Congregationalists and the Anglicans, from which we get the "No establishment of religion" part of the Bill of Rights, since neither group wanted to tithe, officially, to an enemy church.
Religion is a nice basis for morality, but it isn't the only basis. Even the religious have their demons, and using religion as a sword is pretty damn dangerous.
Religion is unrighteous and wicked, when it departs from what God has clearly told and demonstrated to us in His Word. That generally recognized at the time of America's founding as it is, now. Obfuscation is merely obfuscation.