Private institutions. George Mason University is a public school and the situation for this professor is actually the exact opposite of what you seem to be claiming here.
If en employee there notified them that they had been infected with a highly infectious disease (think smallpox) and still wanted to go to work, would they have a right to deny that person? If so, what specifically constrains them in a situation like this that wouldn't in a situation like that?
Would you deny a person entrance to your building because they weren't vaccinated against Ebola or rabies?
Why the different answers?
For example, I generally support laws that let people go topless or nude in public. But I’m okay with places banning people due to clothing choices… like all white conical hoods.