In our school, and bearing in mind a couple of the head Pilgrim Fathers come from nearby villages, we were taught, in so many words;

Americans celebrate the freedom to religiously persecute others without interference, as this was what The Mayflower was all about.

Mind you, when in prison in Boston (Lincolnshire UK) Brewster wrote a letter to someone saying people should have faith in armies to protect them and shun weapons. A copy is on the wall of The Pilgrim Fathers pub in Scrooby.