A health care worker with covid when they should not have it because of access to vaccines is a potential super spreader vector to others that are not yet vaccinated or for whatever reason can't be. So to me that goes against the hippocratic oath. At a minimum they should have to disclose they are not vaccinated so patients can choose not to be around them. Though as others have said it sends a bad message to others that need it more. E.g. if I am a 25 year old that doesn't want to risk the side effects, 70 year olds with a heart condition and asthma that also decide against it with a very different risk profile have made a decision based on the young health worker...
That being said certain people like the pregnant woman that feels we don't have enough data if there are any I'll effects on that particular group seems relatively valid.