One of my paternal ancestors was a King’s administrator and signatory to the Mayflower Compact. He was also the negotiator with the indian tribes, having done the same during a brief stay at the Jamestown colony. He was a hell-raiser and did not adhere to the tenants of the Pilgirms and was frequently in trouble with some of their elders but was a friend of John Bradford. His gravesite and I believe his house or a replica of it are still located in Plymouth.
Not everyone on the Mayflower was a Pilgrim or a socialist which is one reason why they threw out the concepts after about a year of starvation.
Most of the colonies were corporate ventures where the colonists worked for the corporation as employees. They were expected to produce products to be sent back to England to offset the investors investment.
The religious groups were generally of sects that belived in a congregational approach to their religious governance. Similarly, land was divided (at first) so that people had shares in livestock and a division of strips of land (of various quality) according to how many were in the household. Eventually, this system proved unworkable as farming operations were fractured.
I believe this “socialistic” trend contiunues to this day in New England and is why so many of those states are so liberal.