Men would only choose their riders gender for bigotry reasons

That’s not necessarily true though. Many men also feel more comfortable with another man in a variety of situations. Prostate exam, counseling, and barber are all good examples. Some guys are just super awkward with women and might not want to feel awkward while paying for a ride. Hell with the severity an accusation of wrong doing can have some men might not want to ride solo with a woman they don’t know.

The same goes for women, not all women choosing this setting are doing so for safety, sometimes people have a preference. Uber is organizing willing independent contractors to the preference of paying customers. If the customer states they want a specific gender as their driver I don’t see why that would be a problem so long as both parties are fine with that.