No, Taxis are not a form of public transportation.
Why not? What defines public transportation? Is it the size of the transport vehicle? Must it be run by government? What qualifies as public transport, in your definition?
I submit that taxis serve the general public, therefore they are a form of public transportation, and cannot be allowed to discriminate. Like restaurants - when was the last time you saw a Muslim's only restaurant?
If this were a case of white taxi drivers refusing any but white passengers, what would the outcry be? If Muslim cabbies were to discriminate against Jewish passengers, would that be OK?
Driving a cab involves serving the public, and in America any discrimination is not to be allowed. If you have a problem with that, don't drive a cab.
America is a country where the U.S. Constitution is the Law of the Land. We practice freedom of religion, speech, and press. If anyone has problems with that, then they shouldn't live here.