There is a big difference between Puritan New England, and an old England (let alone the other nations in the British isles) where fanatical Puritans have taken over the government, backed by military force, and use it to force puritanism on everyone.
At least in the first decades, people settled in New England because they wanted to settle in a place away from England and its politics, along with other like minded people. The only outsiders they had to deal with were Indians. Everyone else were Protestant religious fanatics. If you really thought differently, you could always move elsewhere in New England and found your own colony, like Rogers Williams did.
Very different in a place that still has large groups of Catholics and non-Puritan Christians, people who still like the traditional forms of government or things like civil liberties, and a King in exile that dissidents can rally around. Plus there is a difference between having France and the Netherlands as neighbors instead of New France and New Netherlands.