If people drank beer to avoid contaminated water, did Puritans drink beer?

I defer to /u/JohnnyJordan's answer refuting the fact that people avoided water in favor of beer in medieval times, and it is a myth.

But as to the second part of your question, yes, the Puritans absolutely drank beer. But it wasn't to avoid contaminated water. It was done for fun, or by social custom anyway. Drinking alcohol was widespread enough that the colonial governments enacted many laws back in 1600s New England to regulate its sale.

There is another myth that /u/JohnnyJordan didn't touch on, which is that the "Puritans" were a teetotaling killjoy religious movement. They weren't. The Puritans weren't only a religious movement. They were a political movement. Religion and government in the 1600s were very much intertwined, which leads to some confusion. The head of the Church of England was the King of England, and the Puritans were one of three main political factions in England at the time. In addition to the Puritans, there were the "Papists", or Catholics, who thought that the King of England's split from the Roman Catholic Church was a step in the wrong direction. Then there were the "Protestants" who were aligned with the King, who supported the King's political and religious position with regard to the church and other things. And then there were the "Puritans", who thought that the King of England hadn't gone far enough, and the split from the Catholic church was just replacing one corrupt organization with another. Their movement was to purify politics and the church from "Romish" or "Papist" positions, which they thought the Protestant position hadn't worked hard enough to remove from English politics, and the corruption of the church-government organizations had, thus, continued.

Though the political positions of the early 1600s obviously don't neatly align with today's politics, at the time, the Puritans were seen as the left-wing political-religious movement in England. The Papists were the conservative right-wing political-religious ideology. And the Protestants were more or less the centrists.

I have written about this previously here, with sources.

The point I am trying to make is that the Puritans were not at all a right-wing, everything-fun-is-forbidden movement. A better way to view them is that what they permitted either came from the words in the Bible, or else came from a bottom-up movement from the congregants. The Puritans were congregationalists--"of the people, by the people, and for the people" in America is an idea that came from New England, from their position that the people's relationship with God and the Bible usurped any top-down decrees and regulations made up by the Pope and forced upon the people against their will.

So what does this have to do with alcohol? There's plenty of alcohol mentioned in the Bible, and the congregants of the Puritan churches liked to imbibe, so it was absolutely sanctioned and allowed under law in Plymouth and the other Puritan-led New England colonies.

Going back to primary sources, here is a law enacted in Plymouth in 1636 regulating the sale of alcohol (punctuation and spelling updates are mine, to make it more clear):

"It is enacted by the Court [i.e. the Plymouth colonial legislature] that none shall be suffered to retail wine-strong waters, or beer, either within doors or without except in Inns and Victualling houses allowed, and that no beer be sold in any such place to exceed price two pence the Winchester quart...

On that same page, you'll see laws passed in the 1630s and 40s forbidding tavern-keepers from serving children and indentured servants; and for tavern-keepers to be drunk themselves while serving alcohol; and for young men to take up permanent residence in an inn if they had another residence in town (presumably from stopping men from getting so drunk at the tavern every night that they couldn't make their way back home).

In 1669, another law was passed in Plymouth, again regulating the sale of alcohol:

"It is enacted by the Court and the Authority thereof, that none shall sell wine, liquors, cider, or beer by retail in the colony except they have a license; and to pay for their license according to the capacity of the place where they live...Moreover, it is enacted by the Court that all such licensed ordinaries [taverns] shall not suffer profane singing, dancing, or reveling in their houses on the penalty of ten shillings for every default and that all ordinary-keepers be ordered to keep good beer in their houses to sell by retail and that someone in every town be appointed to see that the beer they sell be suitable to the price they sell it for..."

In other words, alcohol was ubiquitous enough that Puritan-led Plymouth enacted a law that you had to have a license to sell it, and that each town had to appoint an alcohol inspector.

That's not to say that alcohol didn't have its detractors. A 1646 law in Massachusetts declared "drunkenness is a vice to be abhorred by all nations, especially for those who hold out and profess the Gospel of Christ Jesus" but conceded that no strict law against alcohol would be successful in taking away that vice, and the substance of the law was to forbid selling wine for outside consumption in amounts less than one gallon. This was presumably so that people weren't stopping in to a tavern and filling up their cup to go out drinking on the street.

The third Governor of the colony of Massachusetts, John Winthrop, likewise lamented in his journal about a man who moved from Boston to Newbury, Massachusetts, where he grew "very disordered, fell into drunkenness, and...violent contention". Elsewhere in his journal, he called out a minister who had moved from Virginia to Massachusetts for "being usually drunken, as is the custom there [in Virginia]".

The TL;DR version is that it is not true that people drank alcohol instead of water to avoid getting sick. But the Puritans absolutely did drink plenty of alcohol, but out of social custom rather than out of health concerns. Part of the misunderstanding comes from a misunderstanding of who the Puritans were--they were in many ways a progressive political movement, which was also wrapped up in religion, since religion and government were all wrapped up as one in early 17th Century England. Some of their religious ideas could be right-wing by today's standards, and even by the standards of their own time, even if their governmental philosophy was, for the most part, quite left-wing for the 1600s.

By the 1630s, the colonial government of Plymouth explicitly made it illegal to serve children and indentured servants in taverns and alehouses, and also made it illegal to sell alcohol outside of taverns and alehouses. And by the 1660s, an establishment needed to have an actual license in order to legally serve alcohol in the Plymouth colony at all. But they were passing all these regulations because it was quite common for Puritans in New England to drink plenty of alcohol.