It never hurts to remember that many of the original European settlers to what is now the US were religious radicals who were forced out of Europe because of their religious beliefs. Their influence lives on to this day
Many of the vaunted Founding Fathers were deists, which is just this side of agnostic. They were probably also puritans but none were Puritans.
As far as I can tell we reinvented religion during various Revivals, and what we came up with has only the faintest connection to the version of Christianity that people came here with. They claim connection to that one particular sect, but without either genealogical, intellectual, or theological descent.
I don't fully understand the actual history. But much of what we claim about it is a myth.
The gist that is taught is that they were one of the first and took a big chance is really all it is. There's not much depth to it as far as adoration of the Pilgrims in the US.
I had to read / find some good documentaries later in life before I really learned about them:
If you watch a lot of TV from both countries you will see a very obvious difference in verbal communication. Americans (of which I am one) are so much less articulate when it comes English.
The difference is striking on The Graham Norton Show: almost every American guest stands out as less articulate. This is just one example. Another are interviews with regular people. That’s where it really became obvious.
If there is a difference in communication skills, I don't think religious history explains it.
The pilgrims lived in Holland for years in exile before deciding to go to the new world. It would seem to take an extreme group of people to do that, but articulate isn't one of the traits I would assign to them.
Forced out? Or wanted their particular version of religion to be 'the only one', (oh, as well as being 'persecuted')?