The Salem witch trials were a blot on 'Christendom' indeed, and I am agreed that, depending on how you define religion, it should not dictate to government. The kings had a different role than prophets did in the days of Israel's kings, yet the prophets had an open door to speak to the kings and remind them of moral principles.

The principle of separation of Church and state was to a large degree founded on the view, as u/pnwhomebrewer points out, that no single denomination (or even faith, both Jefferson and Washington reached out to Muslims and Jews, respectively.) was to have a dictatorial role in a Republic. They had experienced themselves, or had ancestors who experienced, persecution for not being in full agreement with the Church of England, and didn't want that type of restriction on freedom again. Yet they all at least acknowledged the work of God in their midst, and many either professed Christianity, Washington, Adams (both John and John Quincy and others proclaimed themselves to be Christians, and sought to live it out), or valued some of the insights while denying miracles (Jefferson) .