Seems to me that the individual who owns the property should be able to have any rules/conditions they want. If people don't like it, then don't live there.
I think they can. The problem comes in when renters don't keep the rules and it's hard for a landlord to evict them based on personal owner rules. (Such as keeping the place clean, barking dogs, parties, etc.) Unless it falls under state/local laws, a landlord can be stuck with them until their lease is up.
Oh, but all the discrimination laws, rent controls, etc. make it impossible for a landlord to have total control of his own property.
Well, I'd just like to be told "you're too old to live here". That would tell some things about the folks that live there and, again, I'd have more of a choice on whether to live there or not. Unless people are "out and about" at an apartment complex, where a potential renter could see who they would be living around, that potential renter could make decisions more than based on how an apartment and/or complex looks.
While I agree that a property owner should be able to rent to whatever demographics s/he wants to, there are often stipulations as to what a homeowner can do with his/her own house so it's not unheard of. I think the idea behind California's law was that people with children were having a hard time finding a place to live. Given a choice, most property managers would probably not want single parents with children, in particular.
The only instance that I know of that can skirt anti discrimination laws would be a two family owner occupied duplex. key phrase being "owner occupied"