It's not a modern concept, but that is certainly what the modern christo-fascism movement wants people to believe so that they can assert their world view that "the U.S. is a christian nation".

Yes, the establishment clause is based in respect for religion and peoples' right to have whatever relationship with their god as they see fit. However, you would have to ignore everything that Jefferson and Madison wrote on the subject wholesale to come to the conclusion that you (e- and Mr. Hamburger) have.

https://en.wikipedia.org/wiki/Separation_of_church_and_state_in_the_United_States

Simply on the face of it the establishment clause states that "Congress shall make no law respecting an establishment of religion". If the state funds a religious school, how is that not the state "establishing" - by the very definition of the word - a religion?

Regarding a U.S. state "historically" being able to buck the Constitution and establish a religion, you'll have to throw in ignoring the 14th amendment... unless to you "historically" & "modern" mean before & after the Civil War, in which case if you're saying that things were somehow better before the war then I've got really nothing else to say to that nonsense.