In the United States, the authority of state governments to mandate vaccinations is clear — it goes all the way back to a 1905 Supreme Court case that upheld a Massachusetts law requiring vaccinations for smallpox.
Vaccine mandates will prove controversial, to put it mildly, but, like seat belt laws, drunken driving laws and motorcycle helmet laws, they will save lives. We should not grant an unreasonable minority the power to endanger public health.
It is far past time to put the health of the public, as a whole, over that of the individual. Don't want to get vaccinated? Fine. Unless you medically are unable to, then you are no longer welcome or allowed in public spaces.