Everything you think you know about the history of the concept of "separation of church and state" is almost certainly wrong.
Mark Bauerlein helps lead the re-education effort in a post at First Things called Public Schools and the Wall of Separation:
The wall-of-separation surfaces again in the 1840s, Hamburger recounts, when nativists regarded the influx of Irish Catholic immigrants with alarm and disdain. They leveled the phrase “separation of church and state” in order to restrict Catholic voting, in particular, claiming that Catholics would vote according to the dictates of Rome, not American principles. They used the argument as a way to limit public funds for Catholic schools, too, and to keep Catholics out of the teaching profession (Protestant schools enjoyed public funds and Protestant ministers as teachers). Nativists advocated public schooling, Hamburger says, “as a means of homogenizing the population in the name of ‘Americanism.’ They explained that public schools would inculcate separation of church and state. That’s why everyone has to go to public schools, so Catholicism would be knocked out of them.”
Such nativist organizations were influential throughout the century and into the twentieth century, and the most powerful of them was the Ku Klux Klan of the 1910s and 20s. The Klan of those years was virulently anti-Catholic and it embraced the wall-of-separation point. (Hamburger doesn’t say so, but the Klan in the 20s, in some estimates, claimed five million members, and states with the highest membership were Indiana and Ohio.)
A leading member of the Klan in his earlier years was Supreme Court Justice Hugo Black. He was third in command of the largest Klavern in the United States. It was Justice Black, of course, who revived Jefferson’s line and planted it into American jurisprudence. “Black used his opinion in Everson to secure the phrase ‘separation of church and state’ in Establishment Clause jurisprudence and this prejudiced phrase has remained there ever since.”
And caused irreparable damage to the place that religion should have in the public square.