It’s easy to stereotype the Puritans because of their religious (and perhaps political) conservatism. Where do these stereotypes get it wrong?
The stereotypical image of the Puritans is of a colorless, bland people who considered anything remotely similar to "fun" as sinful. This image is quite wrong. The Puritans engaged in any number of activities which are all but "puritanical." They wore colorful clothes, ate, drank alcohol, listened to secular music, danced, and made merry. The key was moderation; they were encouraged to do all things in moderation except they should "zealously aspire" to piety.
Sex within marriage was not only considered a good thing, one could be expelled from the church for not satisfying the sexual desires of one's spouse:
which failure to satisfy denies all reliefe in Wedlock unto Human necessity, and sends it for supply unto Bestiality.
Sex outside of marriage was of course condemned, and repeat offenders were made to wear a large "A" on their clothing, literally a "Scarlet Letter." Similarly, those guilty of getting habitually drunk were made to wear a large "D." Yet consumption of alcohol in moderation was not a sin, but a quite proper pleasure. Rev. Increase Mather discribed it this way:
Drink is in and of itself a good creature of God, and to be received with thankfulness; but the abuse of drink is from Satan, the wine is from God, but the Drunkard is from the devil.
They were, however, a firm believer in the Covenant of Believers, which precluded democracy. Rev. John Cotton once commented on Democracy:
Democracy I do not conceive that ever God did ordain as a fit government either for church or commonwealth. If the people be governors, who shall be governed? As for monarchy, and aristocracy, they are both of them clearly approved, and directed in scripture, yet so as referred the sovereignty to himself, and setteth up Theocracy in both, as the best form of government in the commonwealth, as well as in the church.
So although their ideas of government were pretty stereotypical, their true lifestyle was not.
The major way in which it is wrong to stereotype Puritans as arch-conservatives is in the fact that their religion is in some ways more democratic than other religions, particularly at that time.
One of the major tenets of Puritanism is that people do not need to be told what to do by a church hierarchy. People are also expected to read the Bible and to have faith in God. Both of these are somewhat democratic. In churches like the Catholic Church and the Church of England, there was a strict hierarchy with lower levels having to obey those at higher levels. This is not very democratic. In contrast, the Puritans had no such hierarchy. In the Catholic Church, people were not expected to read the Bible themselves but only to do as the priests told them. The Puritans were expected to read the Bible and think for themselves to a larger degree.
In these ways, Puritanism was a more egalitarian and democratic religion that you would think given the stereotypical view of them that we tend to have.