Also, this is a minor point but illegal abortions are many orders of magnitude more risky than COVID vaccines.
I strongly oppose broad-reaching government-imposed vaccine mandates, but I strongly support a vaccine mandate for healthcare workers specifically. The US government has already taken on the responsibility for setting employment eligibility standards for healthcare workers, and it makes sense for being vaccinated to be one of those criteria.
I think the two situations are comparable in some ways, and not in others. The "have to do something medical in order to keep your job" part is one of the ways it's comparable. The "bodily autonomy" is another. It's different in that it's not a government mandate. It's different in how it affects others.
So: Did you actually want to engage, or did you just want to give a plausible dismissal?
This is, as far as I can see, the most directly analogous situation. Those who support vaccine mandates, how do you feel about this situation? (And note that this was just an "unofficial" employee mandate - there was no government entity involved.)