Firstly, there are two different related senses of 'puritan'. There's the meaning specifically related to sexual issues, and there's the wider sense of adhering to a narrow and intolerant ideology. But the two do seem closely related.
The (real, as opposed to liberal) left in Protestant countries does often seem to manifest a distorted version of the puritanism of that wider Protestant culture - far left sects have been known to ruthlessly police the lives of their membership. And nobody has a stronger 'Protestant work ethic' than an ultra-leftist, running around selling papers and organizing meetings 24/7 as if their life depended on it. That's how they get to take over states and parties.
But that's the actual left, not liberals. The Chinese Communist Party, for example, has always had a strongly puritanical streak, in both senses of the word (and Mao having been - by some accounts - a full-on Weinstein, just makes that all the more consistent with puritans of all political persuasions. It's pretty normal for the puritan-in-chief to turn out not to be following their own rules, see also any number of conservative Christians or Islamists).
The differences are in what people get puritanical about. Libertarians seem to get decidedly puritanical about the finer details of private property rights and contracts, for example.
Also, Liberals, being in the middle, can display puritanical traits from either side of the spectrum e.g. Tipper Gore and her parental advisory notices. And insofar as people are non-puritanical, they tend to lose.
The awkard fact is, in many situations it's only the puritans (in the not-specifically sex-related sense) who are at all effective. Look what happened to the Mensheviks or the centrists in 1930's Germany.