And yet they can require many things of people that are infringements of rights of expression and autonomy, such as dress codes.

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 had Ebola or rabies?

Would you deny a person entrance to your building because they weren't vaccinated against Ebola or rabies?

Why the different answers?

I think it’s okay for a public venue to deny people access due to something being present, but not due to something not being present.

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.

Those are exactly the types of things I'm trying to get the GGP comment to elucidate on. Mine was not a comment making a judgement, but seeking clarification on reasoning, by providing a case many could and would agree on to contrast against, in a similar vein to what you attempt to be doing.