Soon after arrival in the colnies, "Puritan Separatists" back in Merrey Olde Englande, chopped off the head of King Charles I, installed their own"Lord Protector" Oliver Cromwell as head of state. That theocracy went so badly they ousted Cromwell, and reverted to monarchy under King Charles II.
It would be over 100 year slater, when at the founding of our Republic, both monarchy and theocracy were rejected.