I think that is already in place. It opens a can of worms: the Muslim drivers get their way, then redneck drivers can refuse to take blacks, etc.
Do you think there would really be a shortage of drivers willing to carry blacks, even if the only penalty imposed upon drivers who refused was to lose their turn in line?
I don't know much about the economics of airport cabs, but I suspect the cost to a cabbie who forfeited his turn in line would exceed the hassle imposed on the passenger who then had to wait an extra five seconds to take the next cab.
At the civil rights museum in Memphis, there's an exhibit that talks about how a city used minimum-fare rules to prevent black-operated cabs from undercutting the fares charged by white-operated ones. Interesting that people have lost sight of what minimum-price laws do.
I would suggest that free markets are far better than forced-association laws in combatting racism and discrimination. To be sure, sometimes higher levels of government need to act to protect markets that may be attacked by lower levels, and even when unfettered free markets won't end discrimination overnight, but they will tend asymptotically toward a playing field that's more fair and balanced than anything the government can produce by fiat.