But it is also worth remembering that the way many Americans tell their own story is mythology from the outset.
For instance, the notion that the Puritans came to America to create a nation in which the idea was freedom to worship as you wish is ... arguable.
The Puritans wanted to worship as they wished and they wanted everyone else to conform with their ideas. Winthrop's shining city on a hill was a beacon of Puritan conformity, not of multicultural welcome.
The reason their movement eventually failed in England was partly because folks tired of their demands for conformity and partly because so many Puritans vamoosed to America.
In America, Puritans didn't welcome other protestants and protestants didn't want catholics to be free to practice their version of christianity in America. The arguments over different interpretations of christianity played out through various colonies: the Massachussets Bay, Rhode Island, Maryland and so on.
The idea of religious freedom wasn't so much an American idea as an Enlightenment one. But that idea didn't spring from the head of Enlightenment figures fully clad. It has a long history, which can be traced back at least to the Church Council at Nicaea under the Roman Emperor Constantine, where the outline of orthodoxy was established after alternatives were expressed. The gobstopper of orthodoxy was released for various reasons, which included the power claims of kings against the papacy, the expense of catholic taxes and the arguments of science. So that by the eighteenth century, the philosophical positions justifying at a minimum religious tolerance were fully formed. Such ideas were well suited to an environment which prized, and demanded, muscular individualism.
The Founders of the United States of America were enlightened enough to take the plunge in favour of religious freedom. In this way, they performed a bold national experiment. But it is one of its time, and not consistent with the idealised version of the history of the pilgrims, so that freedom of worship is claimed as a tale of indigenous virtue from the beginning, in contrast with the wicked conformities of the rest of the world. Mythology simplifies. History is complicated.