The idea of separation of church and state was anathema to most Puritan leaders, including John Winthrop, who governed the Massachusetts Bay colony for the first two decades of its existence. One way in which the leaders of the colony attempted to maintain Puritan values was by limiting the right to vote to people who had gained formal admission to the Puritan church. Anglicans, Quakers, and other dissenters were not eligible to vote or to serve in government. The Puritans also actively pursued Dissenters, especially Quakers. Dissenters were executed, publicly humiliated, fined, and chased from the colony, a fate suffered by both Anne Hutchinson and Roger Williams. Community leaders also tightly censored printed material in an effort to squelch heretical ideas.
Ultimately, the Puritans were unable to attain the degree of control that they wanted. This occurred for two main reasons. First, the colony experienced a constant influx of non-Puritans, including whalers, fishermen, and indentured servants who had little interest in creating a "city on a hill." Second, there was intense disagreement between Puritans themselves. As historian Alan Taylor observes, "without bishops and crown to struggle against, Puritans quickly discovered their many disagreements."
Historians used to argue that Puritans had lapsed from their original unanimity and become less committed to their original mission. The traditional narrative has been that Puritanism declined. Yet most historians today argue that much of the Puritan spirit remained, and that the culture evolved in response to the influx of new ideas (and religious apathy) from without and critiques from within.
Source: Alan Taylor, American Colonies: The Settling of North America (New York: Penguin Books, 2001) 181-185.