No, they were English protestants. But England had a king deciding what everyone had to believe in, the Anglican church aka the Church of England. So they went to the Dutch Republic, often referred to as Holland, which had invented freedom religion and therefore became independent of the king of Spain, at the expense of an 80-year war. But these Puritans didn't like life in the Dutch Republic, because it wasn't freedom of religion they liked. They experienced the Dutch Republic as too free, having a bad influence on their kids. So they left the city of Leiden in Holland to get on board of the Mayflower in England and head for the new world to start puritan settlements there without beeing exposed to other religions and ideas.
Sounds lovely, but it's very unlikely. Contrary to popular belief, the Declaration of Independence wasn't very new, to be more precise, it's central idea's were 195 years old and already written in the Dutch Declaration of Independence of 1581.
Thomas More was already dead before the first settlers in North-America (where do you get those sources?), Locke wrote his important work in the Netherlands, just like many philosophers of the enlightment like Descartes, Voltaire, Erasmus, Spinoza worked there because of the freedom of speech, or had their books printed there because of the freedom of print and press. Many others visited to find out about life in that prosperous republic. So I'm afraid the American DoI didn't need any native American wisdom.
It might explain why the Native Americans got along quite well with the Dutch settlers in New Netherland (today's New York mainly), especially at first. The Dutch were just traders, not rulers, and the settlement was modelled after the Dutch Republic. The Native Americans liked to trade too and had a lot of fur on offer for for example metal tools, it wasn't without troubles throughout the whole time, but they respected eachother for fair deals and keeping their word. With freedom of religion and speech, citizenship, equality and egalitarianism, women were also very free in the Dutch Republic to the amazement or disgust of foreign visitors, so they had that in common. It was a very multicultural and multiracial settlement with all kinds of Europeans, Asians, Native Americans and Africans. The first blacks in North America were most likely free because the Dutch brought them very early and considered slavery unchristian until 1636. Officially at least, but New Netherland was run by the WIC, a semi military trade enterprise to take the war with mainly Spain and Portugal at that time to the seas and cut off the money to finance the war against the Dutch Republic, so the settlement and all the WIC's ships were official and government controlled. If a Dutch ship would capture a Spanish or Portuguese ship they were allowed to take it's cargo, but the slaves had to be set free and would be de iure free when setting foot on Dutch soil. Because of the high death rate among sailors and because you couldn't just leave people on some unknown shore to die, a lot of them ended up beeing employed by the WIC. There are records showing blacks in New Netherland negotiating wages, marrying in Church and owning farms.
So it's the Dutch legacy that shaped the DoI, either through the remains of New Netherland, or through the philosophers of the enlightment, or just by translation of the Dutch declaration of independence. That's of course not the story the WASP's tell you, the victors write history and the Dutch were forced out by the English. The Dutch took the wrong moral turn by themselves, urged by the aggression of all the kings from Spain to England that wanted to end the Republic for obvious reasons, but not forced. Idealism and rightiousness had faded with incredible wealth and the grim realities oversees. They became a slave trading colonial power only slightly better than the English later on and in the 19th century they were even behind on the English when it came to abolition.
But still, makes you wonder what could have been if it wasn't the English but the Dutch who ended up shaping North-America. Don't know about slavery, but the Native Americans would have been better of because the Dutch held them in high esteem and didn't have this desire to rule as much land as possible. It certainly wouldn't have become such a prudish country and 200 years were waisted on English feudal thinking and class mentality, from which it's only a very small step to racism.
