The Puritans (of whom the Pilgrins were a subset) were pissed they couldn't impose their particular brand of theocracy on everyone else, and went to Massachussetts so they could.

Rhode Island was founded because they had serious problems with Roger Williams's unfathomable notion that civil magistrates shouldn't be enforcing religious mandates, and basically exiled him.

The Pilgrims came to America from Leiden in the Netherlands to escape England's mandatory church attendance?

Yes, because they didn't want to be Dutch. They wanted to be English and free to practice their faith.

Pretty much, yes. They were Nonconformists who didn't want to attend services in the Established church, which they considered too popish.

Why were they in the Netherlands

I am worri3d about the puritans, and how they ended up in the netherlands