What if somebody started a Whites-only gym because it made them feel safer?
Maybe some claim it's for safety but the fact they're often 24hr would decry that.
Uber is a public accommodation. It cannot discriminate based on sex. If someone wanted to start a private club where women joined to drive and be driven in a not-for-profit way, that would also be legal.
For anyone reading who has not previously considered it, please imagine what it feels like to be in a moving, locked vehicle you're not in control of, in an unfamiliar place, with someone who is much stronger and taller than you who's not respecting your verbal boundaries. What guarantee do you have it will stop there? What could happen if I truly upset him? How much more unpleasant could it become for me? Meanwhile, I'm paying for this. Even with the option, I'm still paying with the extra time I willingly choose to wait.
Hints: membership clubs, religious organizations (Gainz Я God)