The litigious nature of society is what makes employers think they need to do this nonsense. They're worried about somebody getting sick and somebody trying to take advantage of the system and suing them so they're doing everything they can just to have the appearance of acting good. In today's world, you have to cover your bases to avoid risk of stupid lawsuits even though diseases are a fact of life and there's no way to prove that you got sick at work and not shopping at the grocery store.

If you absolutely need a job that mandates this and can't take a stand on principle, my advice is to offer to sign a liability waiver that you can't sue them for any Covid related problem. That wouldn't completely guarantee that they'll accept you back (some hysterical employee there might think you're a Covid risk or whatever and spazz out) but it's worth a shot.