Displaced in terms of total population, but the aristocracy of the US was mostly Mayflower types will into the 20th Century.

I think some overstate the influence of Radical Protestants on American ideology with offhand references to Max Weber or by calling whatever their pet cause is a fight against "secular puritanism." On the other hand, I do think there are some interesting parallels.

For example, one could argue that the mistreatment of colonists by the mother country was overstated by a population already distrustful of the Crown. I'm no expert, but it would be interesting to read more about that dynamic.

IANAH but I'm not sure one can really separate "treatment of the colonists by the British Empire" from the struggle between Dissenters and the Established Church. Yes, Puritans were relatively few in number but they were influential. Later colonists would have had to fit themselves into the society created by the Puritans, if nothing else by constituting their own power base in opposition to the Puritan one. They are still part of our foundational myth and buckle-shoe-wearing caricatures of them /still/ go up all over the country every single November.