As of right now, it appears that it is legal for employers to mandate employees receive the COVID-19 vaccine. There are exceptions for documented medical reasons and religious reasons though. It’s kind of like how hygienists are required to have a TB test and have several vaccinations or how medical professionals (nurses, doctors, etc.) are required to have a flu shot – it’s to protect not only the clinicians, but their patients.
https://www.natlawreview.com/article/eeoc-publishes-guidance-employer-mandatory-covid-19-vaccination-policies-us
Each dental office will have or has their own policy on whether they will require employees to be vaccinated. From what I’ve seen, opinions on this are all over the place. Some hygienists think its a good idea and some don’t.