[semimojo]

According to you, I have the right to set up a booth and demand proof of vaccination before allowing them access.

LOL. An easement gives them a legal right to access the property. Who has a legal right to enter a Target store uninvited?

[Honest Nigerian]

Answer to your question is based on Civil Rights!
Any of the following can enter: a black man, a white woman, a blue man who says he is a pink woman.
Get the idea?
It would be a Federal crime to prohibit someone from entering a business that is open to the public. We tried to do this with HIV-AIDS.

[GreyHoundSailor]

At the point you describe, there will be ‘the law’ and ‘local law’ - care to guess who’s going to win in a rural community?