In the meantime, warfare and Europe herself underwent a transformation - from a battle of religions it became a battle of dynasties, of nations in a sense. Catholic fought Protestant in what was to become Germany for the seat of Holy Roman Emperor in the beginning; in the end the Protestant Swedes and the Catholic French fought all of the others for their own ends. Certain areas in Germany experienced a depopulation of 50% or more. Villages, towns, all dead, burnt, gone.
If we are to understand the Pilgrims within the context of their own times, that's what we have to digest. It was on the crest of that wave that they entered the New World. Starvation, torture, mass and individual murder - that was truly the currency of the time. I don't know if that excuses the funny hats, though.
With no hope of tolerance in England and continental Europe exploding, why not take a chance on the New World?