Tell me, where do the rights of private citizens end, and the rights of businesses begin?
Businesses are "private citizens", since it is just such citizens who own them.
Your question is no different than: "Where to the rights of my neighbor end and mine begin?"
I think it is more a question of private property owners rather than business owners.
The real question is: where do the rights of private citizens end, and the rights of private property owners begin?
Clearly, the rights of private property owners trump those of private citizens when the citizens is on the private property, even if invited.
For example; if you invite someone into your home, does the invitee have full First Amendment rights? Can he spout off during the meal, and you just have to sit there and take it? Not in my home, nor would I expect in your home.