Who was assured freedom of worship in the Puritan colony?

There never was a "Puritan" colony as such--Puritanism wasn't even a specific or well-defined sect, so much as reformers and malcontents who believed that the Church of England was too Catholic in tone, or the Scottish Presbyterian Church wasn't severe enough, or that the Catholics remaining in England practiced a watered-down version of the One True Faith. It was a vague term, like "evangelicals" is today, and does not describe one single religion.

Anyway, the ones who left England were called Pilgrims. They fled to Holland, but didn't like it and endeavored to flee again to Virginia. Poor navigation brought them instead to Plymouth Bay in Massachusetts. Puritans were actually a minority on the Mayflower; most of these early colonists fled England for non-religious reasons, and the first wave of pilgrims included the Puritans' servants and employees, who tagged along for business purposes, not religious ones.

Plymouth Colony--later Massachusetts Bay Colony--gave freedom of worship to dissenting English Protestants (Anglicans, Congregationalists, and Presbyterians, mostly). Jews were encouraged to settle in Rhode Island, Quakers in Pennsylvania, and Catholics, in Maryland.