If Moore is doing something that is unconstitutional, then the usage of govt. buildings for church is as well, yet they were used for church well after the First Amendment was passed. As far as I am aware, they were only used for Christian services, not Muslim, Jewish etc.
Jefferson at Church in the Capitol "In his diary, Manasseh Cutler (1742-1823), a Federalist Congressman from Massachusetts and Congregational minister, notes that on Sunday, January 3, 1802, John Leland preached a sermon on the text "Behold a greater than Solomon is here. Jef[ferso]n was present." Thomas Jefferson attended this church service in Congress, just two days after issuing the Danbury Baptist letter. Leland, a celebrated Baptist minister, had moved from Orange County, Virginia, and was serving a congregation in Cheshire, Massachusetts, from which he had delivered to Jefferson a gift of a "mammoth cheese," weighing 1235 pounds." Journal entry, January 3, 1802
Jefferson and Family at Church "In this letter Manasseh Cutler informs Joseph Torrey that Thomas Jefferson "and his family have constantly attended public worship in the Hall" of the House of Representatives. Manuscript letter"
Madison Seen at House Church Service Abijah Bigelow, a Federalist congressman from Massachusetts, describes President James Madison at a church service in the House on December 27, 1812, as well as an incident that had occurred when Jefferson was in attendance some years earlier.
The Old House of Representatives Church services were held in what is now called Statuary Hall from 1807 to 1857. The first services in the Capitol, held when the government moved to Washington in the fall of 1800, were conducted in the "hall" of the House in the north wing of the building. In 1801 the House moved to temporary quarters in the south wing, called the "Oven," which it vacated in 1804, returning to the north wing for three years. Services were conducted in the House until after the Civil War. The Speaker's podium was used as the preacher's pulpit.
Communion Service in the Treasury Building Manasseh Cutler here describes a four-hour communion service in the Treasury Building, conducted by a Presbyterian minister, the Reverend James Laurie: "Attended worship at the Treasury. Mr. Laurie alone. Sacrament. Full assembly. Three tables; service very solemn; nearly four hours." Journal entry, December 23, 1804
The Old Supreme Court Chamber Description of church services in the Supreme Court chamber by Manasseh Cutler (1804) and John Quincy Adams (1806) indicate that services were held in the Court soon after the government moved to Washington in 1800.
Description of church services in the capitol building:
