It was hardly a private letter. The Danbury letter was vetted by the Attorney General of the United States. Jefferson wrote the letter as a declaration on the problems of entanglement of religion and the government. The father of the First Amendment, James Madison, wrote almost exactly the same line in regards to separation of church and state. Madison wrote:

“Strongly guarded as is the separation between religion and & Gov't in the Constitution of the United States the danger of encroachment by Ecclesiastical Bodies.” (Detached Memoranda, circa 1820). He also wrote:

The civil Government, though bereft of everything like an associated hierarchy, possesses the requisite stability, and performs its functions with complete success, whilst the number, the industry, and the morality of the priesthood, and the devotion of the people, have been manifestly increased by the total separation of the church from the State (Letter to Robert Walsh, Mar. 2, 1819)