The not wanting to be treated by the unvaccinated is a bit ???
I'd prefer not to be treated by nurses who are drunks or cokeheads or having risky sex - I know at least one who is a cokehead - but the fact is that as long as a nurse doesn't get busted for it there isn't much I can do to find out the details of their private lives. Nor would it be appropriate for me to be able to ask about their personal habits.
In my shitty authoritarian country I'd have had to given up my library job if I'd not been vaxed, and I know guys who work alone in the woods who ended up having to be vaxxed to keep their jobs - all forced through their employment so as to keep the governments hands clean.