According to Colin Woodard, it was due to 1) everyone learning to read (in order to be able to read the bible for themselves, thus leading to an emphasis on education, and ultimately free public education), and 2) a community-oriented spirituality in which the goal was to improve the community through religion, as opposed to southern colonies, for whom religion emphasized individuals improving themselves. This distinction led to a more communal welfare orientation in New England.

Source: American Nations: A History of the Eleven Rival Regional Cultures of North America

I think you're conflating 18th century Puritan religiosity with modern day conservatism. Being religious in the 18th century was the standard. This does not mean that these religious people fit our definitions of "conservatism."

And, in fact, recent scholarship has increasingly moved away from the portrait of Puritans as reserved folk. I point to Michael Winship's Godly Republicanism and Walter Woodward's Prospero's America. Both books emphasize that Puritans were not anti-wealth nor really reserved (in fact, they had a lot of sex). Further, some historians, like Winship, emphasize that Puritan congregationalism actually created the framework for later representative democracy.

According to Max Weber's Protestant Ethic, by the mid 18th century the Mayflower generation's descendants had become ever more prosperous and chose earthly riches and all its comforts over heavenly riches and their requisite earthly asceticism (hard wooden benches, porridge, etc.), while still retaining the Calvinist nose-to-the-grindstone penny-pinching business ethic that was the cause of their prosperity. This only explains how they became less religious, not how they became progressive, and Weber's thesis is by no means the final word, as it was published over a century ago and has been subjected to criticism ever since.