I'd have to say either Puritan or Separatist you decide:
Puritan: a member of a group of English Protestants of the late 16th and 17th centuries who regarded the Reformation of the Church of England under Elizabeth as incomplete and sought to simplify and regulate forms of worship.
Separatist: a person who supports the separation of a particular group of people from a larger body on the basis of ethnicity, religion, or gender.