Why did separatists come to north America?

They came for religious freedom. And they also wanted to completely separate from the Church.

The Pilgrims and Puritans came to America in family groups (rather than as isolated individuals) and were mainly motivated by a search for freedom to practice their religion.

Explanation:

The Puritans created a deeply religious, socially tight and politically innovative culture that is still present within the modern United States. They expected this new land to serve as a "redeeming nation." They fled England and, in America, tried to create a "nation of saints": an intensely religious and completely just community designed to be an example for all of Europe.