What justification do private property owners have to [discriminate against] citizens based on religion, sexual orientation, gender, race, age, ect.?
I don't see refusing service as a private business owners "right" in a country like America. You have a "right" to open a business, but you don't have a "right" to refuse American citizens equal opportunities/goods/services based on personal prejudices. That's my opinion, I'd like to hear what the supreme court had to say about that..
I'm not sure that analogy fits because of second hand smoke. Being black/gay/handicapped, etc. is something that doesn't physically affect anyone else in a public setting, whereas smoking a cigar would
The private property owner has two justifications. If they are in fact the owner, and as long as they are "owning" their property, but not the property of another, they aren't taking anything away from anybody. Unless you think using your own stuff as you see fit, is stealing from somebody else. They also have not committed an act of aggression, since controlling only your stuff and not the stuff of others, is a neutral act, not an act of aggression.
Ownership has to include control over something, or it no longer means ownership.
The second justification is it is not up to any non owners to determine how another person will use their property. Why is government an exception to this? Governments can and do steal property rights, but there justification comes from a gun, not a reciprocal mutual respect for the right of people to own themselves and control their own property.
As far as legal justification, presently there isn't any. However legal things are statutory constructs and do not have to follow logic, rather they can follow the whims of the electorate. For example, it is illegal for us to own our bodies completely, yet most people here, other than a few known prohibitionists think we all should control our own property, ie, our bodies.
The term "public setting" when you use it is a bit of a misnomer that was created by a legal construction. Public setting could be construed as property not owned by a private individual, like a park, a road, etc. It would be difficult for a person to tell another they can't be there in that kind of a public setting. Why? Because that bigot doesn't own the road, the park etc. I suggest there is something called a "public setting" that has usurped to some degree the definition of private property.