It's sexism, plain and simple.
There's an exception to US anti discrimination laws for jobs that require a certain age/sex/gender/race etc. Catholic schools for example can exclude non-Catholics from being theology teachers, for instance. Actors can be excluded on the basis of race, if the character requires a certain race.
I'm not sure though if this qualifies though. Seems like there would be caselaw somewhere on it though.
Mere customer satisfaction, or lack thereof, is not enough to justify a BFOQ defense, as noted in the cases Diaz v. Pan Am. World Airways, Inc.[6] and Wilson v. Southwest Airlines Co..[7] Therefore, customer preference for females does not make femininity a BFOQ for the occupation of flight attendant.[8] However, there may be cases in which customer preference is a BFOQ—for example, femininity is reasonably necessary for Playboy Bunnies.[9] Customer preference can "'be taken into account only when it is based on the company's inability to perform the primary function or service it offers,' that is, where sex or sex appeal is itself the dominant service provided."[10]"
My guess would be that excludes gender discriminating people driving cars outright. While obviously, as discussed in the article, women may prefer women drivers, the driver being a woman is not functionally necessary to drive a car.
"It shall be an unlawful employment practice for an employer
(1) to fail or refuse to hire or to discharge any individual, or otherwise to discriminate against any individual with respect to his compensation, terms, conditions, or privileges of employment, because of such individual’s race, color, religion, sex, or national origin;"