It's best understood by studying the colonial history in the Church History.
While Lutherans and Puritans and Congregationalists left the Old World to form their colonies in the New World, they generally didn't unite, because they were from different denominations within the same Church.
Those who disagreed with the theology of others within their group, voted with their feet, moved either upstream or down the coast and formed other colonies. Generally they all agreed in the fundamental tenets of the Christian faith, but discerned their differences as different religions. None of them considered paganism a valid religion, but instead a false religion.
All of them had escaped the Old World conflicts which had merged the Church with the State, identifying nations with their faith.
Going back to Bloody Mary and Queen Elizabeth, the Separation of Church and State recognized only good men would attempt to obey they law but there was a difference between Divine Law and man-made Law. Such laws were to control the disobedient and those who would cause chaos within both the Church and the State.
Having voted with their feet, they intuitively understood some believers, became further sanctified by better honing some doctrines of the Church prior to others, but different believers were spiritually gifted differently from one another. This recognized different religions of Christianity as still good faith, but any general good man would attempt to live according to the edicts of both the Church and the State, but shouldn't be criminalized by one or the other for attempting to faithfully abide by both.
Hence the historical meaning of the doctrine of separation of Church and State. It recognized good men would attempt to abide by both sets of laws, and no law should be created forming an enemy between the two.
This is strictly a Christian doctrine.
It is not consistent with paganism. Paganism and other false religions drift towards anarchism on one hand and atheistic legalism on the other, having no qualms in criminalizing those who seek to worship God by His protocols, in part because they reject God and what He provides.
This thread is probably better served if it were to study the differences in colonial thought, addressing the same topic as to the domain of Church and State.
Compare the Bill of rights and Constitutions of Virginia, Massachusetts, Connecticut, etc, where different religions wrote tomes on the role of Church and State.
Some identified the role of Church defining the State, while others expressedly avoided any role of the State which touched upon an authority of the Church.
Very interesting. Thank you.
Given ‘religion’ is the catch-all for Christianity by any name, it seems Judaism might be a casualty of this perspective. In your opinion, was Judaism, along with other ‘valid’ religions, at all a factor in the language? We might have a serious Constitutional problem if not.