Is the popular image of the Puritan as purveyor of an intolerant monoculture accurate?

Recently I listened to the introduction of Russell Shorto's _The Island at the Center of the World : The Epic Story of Dutch Manhattan and the Forgotten Colony That Shaped America_. When he talks about the New England colonies, he uses language such as: > Something was happening that was quite unlike the unfolding of society at the two English colonies to their north, where the _rigid_ Puritans, who arrived in 1630, and the even more _rigid_ Pilgrims maintained, in their _wide-brimmed piety_, _monocultures_ in the wild.—p. 61 (emphasis mine) Given that the Puritan movement was escaping religious persecution in England, it's surprising that in they persecuted Quakers (including executing four martyrs ). Further, especially in New England , they largely dedicated themselves to pious amusements and hard work rather than a broad range of culture. On the other hand, they universally rejected the principle of Erastianism , which justified placing the church under the authority of the government. Many Puritans were Calvinists , but by no means were all. The very name, "Puritan", began as an insult bestowed by outsiders. Did Puritans see themselves as "rigid"? Was their mission to create an island of monoculture on the edge of the American wilderness?