Unvaccinated employees are more likely to be hospitalized or die.
There is some precedent for this. In many states, it's legal to fire someone because they smoke cigarettes, even if they never smoke on company time or on company property[1].
That would mean you could fire a remote employee for smoking cigarettes at home in the evenings, after work ends.
1. https://www.nolo.com/legal-encyclopedia/can-employer-threate...