I’m gonna be very simple on this, perhaps my conservative nature (I bunt in slow pitch softball, LOL!).
1) What are the rules at his place of employment?
2) Are those rules legal?
To me it’s that simple. Anything else is politics, throwing shade, or tangential.
(Pete Rose, for example, isn’t banned from baseball because he gambled; he’s banned because he broke the rule against gambling. This coach isn’t being fired because of his position on the vaccine, he’s getting fired for not following the rules regarding the vaccine at his place of employment).