I'll grant that it's contrarianism for its own sake. But I would disagree with the comparison.

The core value of expressing myself how I choose is being upheld by my (albeit asinine) contrarianism.

The core values of Punks on the other hand can not be boiled down to simple contrarianism or an "anti-mainstream" ideology. And frankly the "anti-woke" Conservative movement is damn near the polar opposite of Punk values. So co-opting the term "Punk" just to make Conservatism sound rebellious/edgy/cool undermines the point of both world views.

Also, being "anti-woke" sucks @$$, while not letting people tell me how to talk F*#ks hard.