The national constitution does not include a seperation of church and state it only includes the freedom of religion and the freedom from the government establishing a national religion like they had in England. "Congress shall make no law respecting an establishment of religion or prohibiting the free exercise thereof"
Seperation of church and state is an idea garnered from a letter written by Thomas Jefferson. Lets get to the context and content of that letter which was a response to concerns by the Danbury Baptists. In 1801, the Danbury Baptist Association of Danbury, Connecticut, heard a rumor that the Congregationalist denomination was about to be made the national denomination. That rumor distressed the Danbury Baptists, as it should have. Consequently, they fired off a litter to President Thomas Jefferson voicing their concern. On January 1, 1802 Jefferson wrote the Danbury Baptists, assuring them that "the First Amendment has erected a wall of separation between church and state."
Jefferson's Letter to the baptists said:
"Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should "make no law respecting an establishment of religion, or prohibiting the free exercise thereof," thus building a wall of separation between Church & State. Congress thus inhibited from acts respecting religion, and the Executive authorised only to execute their acts, I have refrained from prescribing even those occasional performances of devotion, practiced indeed by the Executive of another nation as the legal head of its church, but subject here, as religious exercises only to the voluntary regulations and discipline of each respective sect. Adhering to this expression of the supreme will of the nation in behalf of the rights of conscience, I shall see with sincere satisfaction the progress of those sentiments which tend to restore to man all his natural rights, convinced he has no natural right in opposition to his social duties."
As you can see his letter explained that they (the baptists he was responding to) need not fear the establishment of a national denomination. That while the wall of the First Amendment would protect the church from government control, there always would be open and free religious expression of all orthodox religious practices. True religious expression of all orthodox religious practices was protected for true religious duties would never threaten the purpose of government.
The government would interfere with a religious activity if it was a direct menace to the government or to the overall peace and good order of society. (Later the Supreme Court identified potential "religious" activities in which the government might interfere: things like human sacrifice, bigamy or polygamy, the advocation of immorality or licentiousness, etc. If any of these activities were to occur in the name of "religion," then the government would interfere, for these were activities which threaten public peace and safety; but with orthodox religious practices, the government would not interfere).
Today, all that is heard of JeffersonÂ’s letter is the phrase "a wall of separation between church and state" without either the context or the explanation given in the letter Its application by earlier courts is also now ignored. The clear understanding of the First Amendment for a century-and-a-half was that it prohibited the establishment of a single national denomination. National policies and rulings in that century-and-a-half always reflected that interpretation.
And there is your american history lesson of the day.