No it is not.
Justice Hugo Black, when he was head of membership for the largest Klu Klux Klan cell in the South, made new recruits swear to Separation before they were admitted to the Klan. Black was a nativist and anti-Catholic bigot. When he became a Justice of the Supreme Court, he wrote Separation of Church and State into first amendment law in 1947. The Supreme Court in the last two years has not endorsed Separation , whether holding for religious groups or against them. The US Supreme Court has dropped the Separation metaphor, which was never in the First Amendment anyway. They have not yet replaced it with anything. So we had Separation from about 1947-98, not before and not since.
Jefferson was a Unitarian. In many states his church was supported by state taxes. Church services were held in the House of Representatives until after the Civil War. Our first congress authorized the printing of thousands of Bibles and gave land to missionaries in order to convert Native Americans to Christainity. Jefferson attended a 4 hour communion service at the Treasury Department. Even the chambers of the Supreme Court were used for church services.
"Separation of Church and State" is a recent liberal construct. It has no consitutional basis.
You might be interested in an 1802 letter from Thomas Jefferson to Baptists who were being persecuted because they were not part of the Congregationalist establishment of Connecticut: Jefferson Letter
The 1791 First Amendment says, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press, or the right of the people to assemble, and to petition the government for a redress of grievances."
To me that says keep government out of religion. It also says CFR is clearly unconstitutional. If you use the First Amendment to fight CFR, are you going to ignore the rest of the First Amendment as far as religion is concerned? You practice what religion you want, and I'll practice mine. Keep government (and government schools) out of it.