The answer is going to depend largely on what group you're looking at as well as the time frame when you're looking. Not all puritans are the same, mainly you ended up with two groups. You have sepertists (Brownists) and those seeking to reform the Anglican church from within. Even among those groups there were differing levels of social tolerance.

The Pilgrims, as an example, were sepertists. The Pilgrims were a very insular community and came to Plymouth to actively avoid outside influences. This failed right off the bat because to get funding for the trip they traveled to Plymouth with people from outside their group, who they referred to as the "others. "

William Bradford gives us some clues as to their daily life. He was upset by people wanting to take Christmas off work, he is horrified when they are enjoying themselves and not in all day prayer. Just a single example, but it gives a sense of how seriously Puritans took things.

Meanwhile in Massachusetts, you have men like John Winthrop. Winthrop did all he could to keep religious and political hegemony in the colony. Anybody who had beliefs that were not in line with his was labeled a heritic and found themselves in real danger. Roger Williams and Anne Hutchinson learned this all too well and ended up in Rhode Island. Winthrop was not above hanging people with differing views, as he did with a handful of Quakers in the 1660's. Winthrop was a very devout believer in the Puritan cause. He didn't take it lightly, nor was he happy to see anything that would divert Massachusetts from being anything short of the City on the Hill.

Now, an argument could be made that Winthrop was acting with an ulterior motive, namely maintaining the status of the puritans in the colony as a political rather than religious move. However, while there may be truth to that point, it's hard to deny that Winthrop wasn't fully committed to the Puritan cause. That's likely outside the scope of your question and more then I'm going to type on my phone.

As time moves forward and the colonies diversify so to does the standards in different areas. At least initially however being a puritan in the American colonies did come with a very strict set of rules.

According to D’Emilio and Freedman, Intimate Matters, there was very strict community policing of sexual norms — whether you had extramarital sex was everybody’s business — but this was coupled with the fact that after you’d been publicly punished, life went on as normal and nobody really held a grudge. So depending on your sensitivity to public punishment, you might decide the sex was worth it. In fact, many young couples used this to force their parents to assent to a marriage — they’d just have sex until they got pregnant, publicly confess, then get married.