I assume he means the right to not have a substance injected into your body if you don't want it.
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.