It's an interesting problem. If a venue owner rents to anyone, they're obligated to rent to everyone?
I can see this being complicated. One venue owner won't want to host a show because of the race/religion/ethnicity of a comedian. That would be a problem. But what if a band has a reputation for riling up crowds until they riot and tear places apart? Is it a problem for the venue owner to refuse to let them have a show? What if the potential violence isn't as direct, like the venue is threatened with a boycott if a person is allowed to hold a political rally there? Should they be allowed to deny that rally?