Actually what the Amendment clearly states is that Congress does not have the power to impose a religion on the federal level. The intent was to protect individual states and their religions and reserve the option of declaring an official for themselves, which some did.
Here's some additional info, more detailed that I can pretend to do:
https://religionandpolitics.org/2013/04/09/north-carolinas-official-religion-the-convoluted-history-of-american-states-and-established-religions/
https://www.mtsu.edu/first-amendment/article/801/established-churches-in-early-america
https://www.loc.gov/exhibits/religion/rel05.html
Bear in mind, the opinions you posted came from some of the same Founding Fathers who absolutely abhorred slavery yet owned them as well, with the much esteemed Jefferson owning over 600, and Washington over 100, with over 300 at Mount Vernon, including Martha's family from her first husband and 40 rented because, hey, at least he was disgusted by it, so it's the thought that counts.
That's the same George Washington the Founders wanted to crown king, they who appointed our first 14 presidents (8 under the Articles of Confederation), and who only reluctantly granted the right to vote - and that only to rich land owning WASPs (which, incidentally, tended to translate into slave owners as well to rub some salt into that bucket of irony) - instead of reserving the right to appoint for themselves - the neu aristocracy - as they saw the common man as too stupid and lowly of class to warrant the right to vote. Frig, it's amazing that the glorious sainted founding fathers didn't simply declare themselves overlords over the peasant masses.
So, yeah, they tended to not think highly of religion just as they didn't of the lower classes who adhered to it. But at the same time, Jefferson & Co saw its value as a tool to help provide them a common culture, something to unite them around, supply them a morality. People are bad enough WITH religious beliefs, can you imagine how the dunderheads would act WITHOUT it to keep them in line?
The Founding Fathers saw how easily British subjects were willing to revolt against their king, last thing they wanted was for them to be turned on next, with no Atlantic as a moat should their new charges go French style on their lovely wigged heads.
So concessions were made: voting, and yes, religion. Let people think you've granted them some control over their lives and they will do anything for you,,,