1. Tell them it’s none of their business (if you want to take a principled stand even at the risk of losing out on a job offer).
2. Lie about it (if that particular job is that important to you).
As someone who has worked in senior corporate management roles in the past, I suspect most employers have no interest in the stupid vaccines, may only ask about it (or require you to attest that you got it) to cover their asses legally, and really don’t care if you lie about your medical history.
Because companies love being lied to? Lie in the interview process and your guaranteed to be fired if they find out.