Google also won't employ you if you turn up to your interview with very bad breath. That's not a violation of a right to not clean your teeth.
You're seriously confused about what a 'right' is.
There is no medical secret anymore? Being vaccinated or not should be, and remain, a private decision - with your doctor as a counterpart. Your employer has nothing to do in it.
No I don't think that's a right is it?
I've always had to disclose vaccination status prior to the pandemic to my employer for travel reasons, for example.
Google also won't employ you if you turn up to your interview with very bad breath. That's not a violation of a right to not clean your teeth.
You're seriously confused about what a 'right' is.