Like other groups that sought sanctuary in North America in the seventeenth century, the Puritans desired religious freedom to practice their own faith, but they saw no hypocrisy in not extending that same freedom to people who held other beliefs. In fact, the word "Puritan" was applied to several extremist Protestant sects whose intention was to reform the Church of England because it had become too morally slack. The term was first applied to the group by its enemies as an assignation of contempt for their extremist views.

Puritans believed in studying the Bible and interpreting it as literally as possible; in deeply personal and complex conversion experiences; in the elimination of music but the importance of sermons during religious services; and a strict structuring of family life, with husbands as heads of the household.

Although the Puritans squabbled over doctrine in New England, their adherence to strict values enabled them to survive the harsh conditions in which they found themselves. Without the disciplines that their religion imposed upon them, they might have succumbed to the rigors of the New World, like so many other failed colonies. However, their adherence to their beliefs left them extremely intolerant of others. Government laws included mandatory church attendance on Sundays. To protect society from moral faults such as heresy, punishments, including banishment from the colony, corporal punishment, and the death penalty, were used.

As mentioned above, Puritans saw no hypocrisy in the forced imposition of their values upon the populace of their colonies. In fact, they believed that it was their moral and ethical obligation. The viewpoints of other colonists on the Eastern Seaboard differed, and they may have seen the Puritans as hypocritical. Sometimes, non-Puritans, feeling oppressed by the strict Puritan regulations, left New England or were expelled and sought places in colonies further to the south.

This question -- how can one reconcile the pursuit of religious freedom through emigration with the intolerance towards others demonstrated by these settlers to the New World -- is quite interesting, as it illuminates in its own somewhat tautological way the fundamental hypocrisy surrounding issues of tolerance. Many refugees from politically, ethnically, and religiously intolerant regimes bring with them to their new homes the same levels of intolerance they had sought to flee. This by no means suggests that all such immigrants carry this type of moral baggage, as many justifiably fled repression with legitimate hopes of greater freedom to practice their religions of choice without simultaneously harboring prejudices against others. It is, however, an acknowledgement that certain immigrant communities throughout history have condemned as inferior those whom they did not understand and whom they sought to marginalize just as they themselves had been marginalized or repressed in their lands of origin. The first European settlers to North America, as the question notes, were fleeing religious intolerance, yet sought to impose their own values and beliefs on those who already occupied the lands these Europeans now held. 

The Puritans -- the mere moniker suggests a sense of moral superiority over others -- were intolerant of the native populations they encountered and believed fervently that it was their responsibility to convert and/or repress these 'lesser' peoples. These religiously devout settlers believed that they were performing God's work in spreading their beliefs and practices to others, and they justified massacres and other forms of repression in the name of God. English army officer John Mason, a leader of the military struggle against the region's indigenous population (mainly the Pequot) famously commented on the massacre of Pequot villagers "God laughed his Enemies and the Enemies of his People to Scorn, making them as a fiery Oven." 

That the practices of the Puritans and other early European settlers could logically be considered hypocritical given their treatment of North America's indigenous populations is self-evident. Fleeing persecution for their own beliefs, they in turn persecuted others. Unfortunately, this phenomenon appears to be part of human nature, as it has been replicated numerous times over the centuries.