I admit I may not be fully up-to-date with the kids genders these days, but I think if you opt NOT to have a woman driver, and NOT to have a non-binary driver, that kinda narrows down who will be picking you up.
Although, I suppose you still need to worry if the man is OEM or Aftermarket.
I don't disagree with that the way you understand it would lead to that being an option, but I'm not sure that your design is the one they've opted to go with.
As I read it, based on the description you can either:
Get the first driver/passenger available of whatever description.
Avoid male drivers/passengers and get the next female or mentally ill male available.
Maybe they're designing it the way you imagine with toggles for various genders and mental conditions, but I think it is unlikely they'd allow any sort of discrimination against protected categories. It is far more likely that there is strictly an "avoid men" flag.