The Baptists were first.
From wiki:
Originally, Baptists supported separation of church and state in England and America. Some important Baptist figures in the struggle were John Smyth, Thomas Helwys, Edward Wightman, Leonard Busher, Roger Williams (who was a Baptist for a short period but became a “Seeker”), John Clarke, Isaac Backus, and John Leland.
English Baptists
In 1612 John Smyth wrote, “the magistrate is not by virtue of his office to meddle with religion, or matters of conscience”. That same year, Thomas Helwys wrote that the King of England could “command what of man he will, and we are to obey it,” but, concerning the church — “with this Kingdom, our lord the King hath nothing to do.” In 1614, Leonard Busher wrote what is believed to be the earliest Baptist treatise dealing exclusively with the subject of religious liberty.[3]
American Baptists[edit]
The Danbury Baptist Association of Danbury, Connecticut sent a letter, dated October 7, 1801, to the newly elected President Thomas Jefferson, expressing concern over the lack in their state constitution of explicit protection of religious liberty, and against a government establishment of religion.
In their letter to the President, the Danbury Baptists affirmed that “Our Sentiments are uniformly on the side of Religious Liberty — That Religion is at all times and places a matter between God and individuals — That no man ought to suffer in name, person, or effects on account of his religious Opinions — That the legitimate Power of civil government extends no further than to punish the man who works ill to his neighbor...”
As a religious minority in Connecticut, the Danbury Baptists were concerned that a religious majority might “reproach their chief Magistrate... because he will not, dare not assume the prerogatives of Jehovah and make Laws to govern the Kingdom of Christ,” thus establishing a state religion at the cost of the liberties of religious minorities.
Wall of separation
Thomas Jefferson’s response, dated January 1, 1802, concurs with the Danbury Baptists’ views on religious liberty, and the accompanying separation of civil government from concerns of religious doctrine and practice.
I thought that jefferson coined the metaphoric phrase.
Don’t know that Baptists ever got to head up a state church.
The story is that John the Baptist was killed in part due to his criticism of the temporal authorities, but not for being a Baptist.