That's obviously untrue. For example the state claims the right to confine (and sometimes even execute) the body of people convicted of murder. And most people are ok with that.
Where the line is, is of course a complicated question, but the absolute version where the state cannot ever control people at all, is obviously false.
When I was 18 year old I had similar ideas, but later I found a great song by the clash that goes by as: “I fought the law but the law won”[1].
Even the rebellious spirit of 70s punk acknowledges that one may fight(and should) but the law wins, and has power over your body however the law says so. To fight the law you cannot use your body but your mind.
This is obviously untrue: the state can lock up and kill you, is currently asserting its right to restrict people from having abortions performed on them, and has been increasingly aggressive about attack peoples' right to undergo hormone replacement therapy, among many many other examples. Mandatory vaccination has very much been something the state has historically exercised its powers to enforce, quite successfully in the case of smallpox.
We're extremely inconsistent about what authority we exercise over others' bodies, generally, but we're a very far cry from never exercising it or acting as if doing so were simply beyond the pale.
Education is hard. Deradicalization is even harder. But it's something we need to learn how to do again as a society.
Some of the vaccine conspiracy theories are truly insane, but medical patriarchy is not the answer.