I would be remiss if I didn't point out that thinkling friend Ancient Mariner has written about Roger Williams as well.

Most people, if they even remember hearing of Roger Williams the Puritan and founder of Rhode Island, have a vague memory of him as an early advocate of religious liberty—usually contrasted with those awful Puritans, about whom we have all sorts of negative modern fantasies. The truth is, yes, the Puritans had some things wrong, but they were a lot better than their enemies make them out to be; and as regards Williams, it’s important to understand not just what he believed, but why.

...

He was, in short, a Puritan extremist, a hyper-Puritan; this was at the root of his argument with Cotton and the other leaders of the Massachusetts colony. Cotton in particular tried to reason with him, denying the need for absolute purity as a precondition for joining the church... According to Cotton, the church did not require people to be perfectly pure to be godly; instead, it took godly people and showed them the areas of sin in their lives. He argued that to impose a standard of perfect repentance for church membership was to “impose a burthen upon the Church of Christ, which Christ never required at their hands nor yours.” Cotton finished by arguing that the presence of unclean people within a church did not make it any less a true church.

As odd as it may seem to us, Williams’ surface toleration was rooted in a deeper intolerance, while Cotton’s support of policies that seem intolerant to our age arose out of his belief in grace... By contrast, while Williams’ positions match those of our own enlightened time, we should look carefully enough to recognize that his support for tolerance was rooted in part in a belief in the spiritual inferiority of those tolerated.

There was indeed a serious rivalry between Cotton and Williams. I think AM knows far more about this subject than I. To me it's fascinating.. They wrote about and to each other frequently.