Many Puritans claimed they came to North America seeking religious freedom, but they were extremely intolerant of other beliefs. In fact, there was greater liberty of conscience back in their Native England. How do you explain this? How did the Puritans use their concept of moral liberty to justify their actions against others in the New World...and why might some Puritans, other English settlers in the New World, and those remaining in England see these justifications as hypocritical?
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.