You need a citation for many women being unsafe with random men in a car but the reverse not being true. OK buddy.

No because the presumption is that you will provide ID to your employer and they will go by whatever is on the ID when assigning rides.

It’s not. You as an employee or contractor aren’t entitled to a particular client being assigned to you against that clients wishes. Customers are allowed to pick their contractor

Many women want to ride with other women for safety reasons. Men would only choose their riders gender for bigotry reasons. There is little reason to enable their bigotry. If fewer bigots ride it’s a bug not a feature.