I disagree with the punk analogy because Zerohedge always seemed decidedly right wing or libertarian at best. Always heard the Ron Paul types talking about it. It’s basically conspiracy theories for economics and finance.
Punk is mostly left-wing with a lot of anti-authoritarian, anti-fascist, pro-feminist, anti-racist themes. There are exceptions to the rule (TSOL), but for the most part it was not right wing. They were on the far end of the spectrum to yuppies in the 80s and have only moved further left. Think of Dead Kennedys, Crass, and other classic punk like Bad Brains. There were definitely nazi-punk and other exceptions, but still a minority.
Downvoters are free to explain why I’m wrong instead of downvoting since they are upset with facts.
I've no idea about punk, but our parent didn't talk about wings but about libertarianism.
I also believe that those themes you listed in your first sentence are there to imply that they are somehow inherently left-wing, which would be a partisan statement.
For example: there is certainly an authoritarian left and an authoritarian right as well as an anti-authoritarian left and an anti-authoritarian right.
But, more generally I think that "left" and "right" do more harm than good for describing political content dimensions.
Historically, punk has definitely been on the left than the right, but I somewhat agree those aren't the best terms (but they are what most use, so I used them). A better way to see the political spectrum is the the Political Circle or Horse-shoe theory. Zerohedge would be in the lunatic fringe area.