Let’s not forget that Puritans used hang Quakers. They left England to establish a Puritan state where Puritan Anglicanism a.k.a Congregationalism could be practiced. They did not leave England to establish a state where people were free to practice whatever religion they wanted. It is incorrect to say the Puritans wanted freedom of religion; they did not. They wanted to be able to practice their own religion freely. Those are two very different things.
Some people prefer to say that the evangelicals are the heirs of the Puritans. In one important way, they are. They are both invisible.