I don't think that's racism, I think that's business. Taking someone from Penn Station to Grand Central Terminal is pure profit, because it's fast and you're guaranteed a fare once you get to Grand Central. Taking someone from low-density area A to low-density area B is less profitable, so you don't see many cabs in these low-density areas.
I see this in action all the time, because I tend to bike late at night when bars are closing and people need cabs. If a cab does end up in Brooklyn, because they were required by law to take someone from Manhattan there, they tend to beeline it back to Manhattan, avoiding streets where they might encounter a fare. Smith St. / Clinton St. is one pair like this. Clinton St. is a residential street that leads to the Brooklyn Bridge. Nobody naturally wants a cab there[1]. Smith St. is one street over going the same direction, and it's all bars and restaurants. It also leads directly to the Brooklyn Bridge (actually, the Manhattan Bridge; they're very close). But you see most cabs opting for Clinton instead of Smith, so they don't get stuck picking up someone in Brooklyn that wants to go even deeper into Brooklyn. Instead, they try to get back to the highly-profitable Manhattan as quickly as possible, even if it means going empty.
That's not racism, that's just the reality of how you make money as a cab driver.
(The cabs that can't pick up passengers in Manhattan all take Smith St.)
[1] Except people like me that have noticed this pattern. I do see cabs stopping for fares on Clinton, since they have to if flagged down.
If it's anything like where I live it's not necessarily monitored or enforced. If you accidentally tell the cabbie where you want to go before getting in they'll just drive off.
If you're already in the cab when you tell them then they're not likely to tell you to get out.
But they're already paying for these underground transit options. So there's clearly some combination of pricing and shared routes at which customers can afford it and the providers can still make a living.
I see this in action all the time, because I tend to bike late at night when bars are closing and people need cabs. If a cab does end up in Brooklyn, because they were required by law to take someone from Manhattan there, they tend to beeline it back to Manhattan, avoiding streets where they might encounter a fare. Smith St. / Clinton St. is one pair like this. Clinton St. is a residential street that leads to the Brooklyn Bridge. Nobody naturally wants a cab there[1]. Smith St. is one street over going the same direction, and it's all bars and restaurants. It also leads directly to the Brooklyn Bridge (actually, the Manhattan Bridge; they're very close). But you see most cabs opting for Clinton instead of Smith, so they don't get stuck picking up someone in Brooklyn that wants to go even deeper into Brooklyn. Instead, they try to get back to the highly-profitable Manhattan as quickly as possible, even if it means going empty.
That's not racism, that's just the reality of how you make money as a cab driver.
(The cabs that can't pick up passengers in Manhattan all take Smith St.)
[1] Except people like me that have noticed this pattern. I do see cabs stopping for fares on Clinton, since they have to if flagged down.