The word "church" in "separation of church and state" does not necessarily refer to a Christian organization, nor is it supposed to. It relates to the building-collectively known as "churches" people go to for religious reasons.
However, by the 17th and 18th centuries of Enlightenment, several political philosophers began to argue against monarchy and hereditary succession as bases for de jure government authority. By the end of that century, religious pluralism had increased to the point where some people were fleeing the religious persecution that remained in Great Britain for the religious freedom of the American Colonies.
The idea of total withdrawal from the political system was later expressed through the separation of church and state doctrine. This was incorporated into the body of law known as the First Amendment to the United States Constitution, prohibiting the federal and state governments from establishing religion, restricting the free exercise of faith, and infringing upon the freedom of speech.
The USA Constitution was born from a so-called "revolution" for independence. This Constitution became a template for many of the world's constitutions, America touting itself as "the great experiment."
Many assume the "separation of church and state" appears in the U.S. Constitution. However, it appears nowhere in the Constitution.
The phrase exists in several of America's state Constitutions, however. The Virginia Statute for Religious Freedom was the first state to limit religious exercise, created by Thomas Jefferson.
The First Amendment is the closest phrase in the U.S. Constitution: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof." This establishes the "establishment clause" and "the free exercise clause." The free exercise clause has had the most impact on discussions about the separation of church and state.
In decisions of the Supreme Court in the United States, dating back to the 1970s, more than 25 separate cases have discussed the separation of church and state. Some cases involved schools. Other cases referred to the phrase as a metaphor. Still, other decisions found that the interplay between state and federal law provided a workable separation of church and state.