Being critical of the state where it does things that impact on people's wellbeing and freedom is one thing - as I've said, I'm not convinced vaccine passports are a good thing, precisely because I don't trust the state to act in everyone's best interests. That's clear to anyone who wasn't born yesterday. But the state has also provided me with, for example, vaccination against covid-19, which is unequivocally a good thing according to the objective data on the risks involved.
But I certainly don't buy that the anti-vaxx movement is only "accidentally" right-wing, or that this is just a result of some failure on the left's part, because while clearly nobody is a priori immune to the disease, it does pose a far greater risk to the very old or people who are disabled or already ill with something else. The stats for covid deaths of mentally disabled people in this country are incredibly depressing, for example. So somebody who thinks (rightly or wrongly), "I'm healthy so I'll just shrug it off, fuck vaccines" - that it's only for the Untermenschen to worry about, in other words - yeah, that's pretty right wing. And whether or not herd immunity is ever really achievable, it's clear that vaccination strongly reduces your risk of catching it and therefore of passing it on, so your own vaccination status has an impact on those around you.