Quite frankly, I don't care what the words mean today, since we have a body of court cases that has expanded the application of the First Amendment beyond the strict scope of the words as they were written.
There are good reasons to believe that's not the sense in which the word is used. The Constitution repeatedly uses the word "establish" in the sense of "to make official."
You keep trying to make linguistic arguments while ignoring the linguistic means of the words at the time they were originally written, especially when one of the men responsible for actually writing the Bill of Rights explicitly stated what the words of the First Amendment were intended to mean at the time they were written.
The First Amendment was explicitly intended to create separation of church and state at the Federal level. Like the rest of the bill of Rights, it wasn't intended to apply to the states at the time, so your arguments about state churches are entirely irrelevant.
Lastly I wanted to mention the parallel term you draw here because it's also a drifted phrase
> to make official
Is actually a highly accurate synonym for establishment, but only in archaic word usage, official (the adjective) is actually just a corruption of official a noun, it's sort of like "the influencer lifestyle" or "that's an influencer hat". Technically all "off-*" words originally related to religion, but that's gone by the wayside quite a bit by now.
Reading "establishment" synonymous with "organization" would be anawkward and un-idomatic even today. Would you call the ACLU a "civil rights establishment?" Would you call NARAL a "women's rights establishment?"
There are good reasons to believe that's not the sense in which the word is used. The Constitution repeatedly uses the word "establish" in the sense of "to make official." It uses the word "establishment" in one other place, referring to the requirements "for the Establishment of this Constitution.” I.e. the requirements to make the draft constitution the official law of the country.
And historically, "establishment" was used precisely in that sense--a religion that had been made official. The Church of England was an "establishment of religion." The Colonies had had "established" churches, and many, but not all, had "disestablished" their churches. “An establishment of religion” is not a weird way to say “religious organization” but a legal thing that existed at the time that made sense to talk about. And what the First Amendment does is prohibit the federal government from making laws with reference to those "establishment[s] of religion."
Within that framework, Congress was probably prohibited from establishing a national church. But why? Is the answer: because established churches were bad in the same way that cruel and unusual punishment is bad? That would be an odd reading given how many of the original 13 colonies had some form of government supported religion. The other interpretation is that the amendment endeavored to protect these establishments from federal interference. That’s what makes the most sense given the structure of the colonies at that time.
Within that framework, incorporation doesn’t make sense. You take a provision that was intended to protect states' rights to maintain their established religions free from federal interference, and turn it into a provision that eliminates the very right the amendment sought to protect. https://openscholarship.wustl.edu/cgi/viewcontent.cgi?articl...