You (quite reasonably) don't want homeless people to piss in public, and you recognize that they don't have anywhere else to piss. I'm not clear why "therefore, give them a better place to piss" isn't your first demand, instead a distant second after "therefore, illegalize homeless people." (Which you know very well is the only possible result of banning people from public spaces who don't have any access to private spaces.)
I am not suggesting that we exclude the homeless from public space, but that we allow everyone else to continue using modes that provide more separation from our broken society while society gets its house in order.
Apartheid is specifically a policy of racial segregation, which has nothing to do with this.
I do advocate a system of segregation from other people's urine, not exactly a protected class (who opposes the use of toilets?), and from each other more generally... what are apartments for, after all, if not to keep us apart? I'm proud to say that I voted in this election for as much apart-ness (i.e. as many apartments) as possible. In fact, since I consider this to be a step towards ending homelessness (by building enough housing for everyone) you could say I am even an agent of the eradication of an entire social group!
EDIT: Yeah, that's a bit flippant. But I do believe people are entitled to choose the company they keep. That applies at rest: everyone should be able to have their own apartment, a space where they decide who gets to come in and who doesn't. It also applies in transit: personal vehicles are best (though bicycles, motorcycles, and scooters are probably better than cars, at least in the Bay Area, because the climate is hospitable and space is at a premium). On public transit, we have an obligation to minimize unwanted interaction: uninvited conversation, physical contact, eye contact, and phone speaker music are all (rightly) taboo. Public transit systems should strive to provide everyone with a forward facing seat so that they are not touching or staring at anyone else.
When people do not follow these rules, and instead insert their presence loudly (i.e. by smell), I do think it's better to go around the problem by taking other forms of transportation, than to muddle through and develop resentment, or grow supportive of police violence to shove the problem away (I've been catching myself sympathizing with this). Abandoning public transit seems like the least shitty approach to the people who make it intolerable.
Apartheid is a top-down system, where segregation is mandated. What he is suggesting is the bottom-up approach, where people can segregate themselves if they want to.
Although in practice this still produces segregation on a large scale, as in e.g. "white flight" in US. But then again, attempts to counter such things by forcing people together - like forced busing - didn't exactly work well.
