The Puritans were one of the groups who left England to find religious freedom in the New World. Pilgrims would also be one of those groups and there were several others.
The Jewish people
To escape religious persecution.
People who specifically came to North America to escape religious persecution in Europe, naturally did not want to create societies in which others would suffer religious persecution, since that would be very hypocritical.
Religious persecution was very importation that caused people to explore outside of Europe and find a place in which persecution did not exist. A primary example is the Protestants that came to America to escape this.
The Pilgrims left their homes in Europe to escape religious persecution. They were seeking religious freedom and the opportunity to practice their faith without interference from the government or religious authorities.
The pilgrams and puritans came there to escape religious persecution.
Britain was not a place for religious freedom. Catholics were persecuted. Anglicans ruled. Some protestant groups were despised. And there were Anglicans who wanted to further change the chruch. A new land offered the chance to worship as you want and change the church if you feel like it.
People from all parts of Europe were trying to escape religious persecution from the Church of England. Colonial America was a destination where they could worship freely.
Refugees is the word. immigrants came to America
Freedom of democracy and infrastructure for living conditions
The first settlers who came to North America came to be free from religious persecution, and to create a "city upon a hill". Once established the persecuted became the persecutors and denounced and cast out anyone who did not follow their religious beliefs. Different settlements over North America often were filled with people who had different religious beliefs, with a few places that offered religious freedom and did not persecute anyone. Religious persecution accounted for some of the killing of Native Americans and fights between different settlements across North America.
One of the primary reasons people left England to come to America was the pursuit of religious freedom. Many individuals and groups, such as the Pilgrims and Puritans, sought to escape religious persecution and establish communities where they could practice their beliefs without interference. This desire for a place to worship freely played a significant role in the early migration to America.