It can, but it's a lousy argument. If my body doesn't affect your body, it should be my choice. Freedom is an American value. It's not a world value, and I wouldn't impose it on other countries, but it is an American one.
I'm 100% for vaccine mandates iff vaccines significantly reduce R0.
I'm 100% against them if they do not. Once my vaccination stops affecting the public health, it's my choice.
Banning unsafe things IS a mistake. Yes, I ought to be able to sword fight on a tightrope with sharp swords and no protection over a pit of alligators, if I decide that's what I want to do.
If that's the concern, then triage the unvaccinated COVID19 patients last. But in the long term, capacity expands to meet demand, and it's perfectly okay to change insurance premiums for anti-vaxers, smokers, or otherwise (or sword fighting over a pit of crocodiles, for that matter).