Under the NYC "mandate", No one is required to be vaccinated. I'll say that again: no one is being required to be vaccinated.
While I disagree with the DeBlasio administration's new policy (WRT bars, gyms, etc.), both because it will be almost impossible to enforce and because the benefits (via increased vaccinations) will likely be marginal at best, no one is forcing anyone to do anything.
I'd much prefer (as an increasing number of restaurants, theaters and other venues and businesses are doing) that requiring patrons and staff to be vaccinated be a decision taken by the specific business involved.
Those businesses that only allow vaccinated people in their establishments will gain some folks and lose others -- and vice versa.
Regardless, and I'll say it one more time: the "mandate" from the NYC government doesn't force anyone to get vaccinated, nor does it restrict anyone from public spaces.
NYers aren't stupid (or at least not in any greater amount than anywhere else) and most will (and have) take appropriate precautions.
That said, the new requirements won't be all that effective because they're essentially unenforceable unless the business' owners are fully on board -- if they are, then they'll (as many have already done) require their staff and patrons to be vaccinated.
If a business' owners aren't on board with this, they won't require it, whether it's mandated or not.
A ball of cells and flesh that cannot survive outside of another human does not and should not have human rights. Otherwise we gotta start considering the human rights of cancerous growths.
If so, we can apply the same logic to coronavirus and pregnancy. If not, you're just drawing a false parallel.
We've had mandatory vaccinations for over a century, certainly since Roe V. Wade, and yet abortion is still legal.
Half the US believes abortion is murder and a sin against God and yet as far as I know, never has anyone tried to use the existence of vaccination laws as a pretext for making abortion illegal. That wouldn't even make sense.