Nice to see you posting again, j-t.
The Puritans got the chance to dominate proceedings in England for a few years in the middle of the seventeenth century. They weren't altogether tolerant of a wide variety of ideas themselves. Amongst other things, they stopped the tradition of dancing around maypoles, which is unforgiveable of course.
The English fought their own battles to establish a measure of religious flexibility in that period. But you also have to remember that religion and politics held hands back then. The pope liked to reach into a country to influence policy, encourage invasions and rebellions, tax people, excommunicate princes, extract confessions and suchlike.
So the idea of "freedom of religion" was something which had more baggage when the pilgrims went adventuring than it does now.
The English still burn a Catholic ritually every November 5th. Why? Because he - Guy Fawkes - tried to bomb the Houses of Parliament for the sake of his religion.
As a twenty-first century American seeking to understand English attitudes to seventeenth century Puritans, you might consider the parallel of the puritan and fundamentalist forms of Islam. In which there's a sense of subversion and actual physical threat to the United States.
Maybe we are a little more tolerant now. And maybe not. Tolerance and virtue are not always synonymous.