I worked in medicine. Some employers mandated the flu vaccine. I have not worked in facilities since COVID and the pediatric home care agency I worked through did not require the flu or the COVID.
Generally, I would say they should not mandate them. Other than medical facilities in the critical care and geriatric areas.
If employers can mandate vaccinations, then they should be responsible for any adverse affects some may have with those vaccinations. Such as death, or some permanent disabilities. Meaning they will pay for their mandate.
Employers love to mandate. If they are responsible for their mandate, what will that do to their insurance rates? Their unemployment payment? Their workman's comp. payment?