Earlier quoted context omitted.
All I'm hearing is carve-outs and exceptions. "But when I do it, it's ok." If you're excluding people based on sex/gender it's discrimination. We either care about sex discrimination everywhere, or we don't care about it anywhere. Everywhere includes public and private life.
All I’m hearing is bad-faith nonsense built on intentionally ignoring the concept of civil rights. Why go on the internet and do this? Honestly. You know that your line of argumentation doesn’t even remotely care about being serious, yet you make it anyway. Why? To waste my time?
What should a woman in this position do? Look at the options and think to herself, "I could choose a woman driver, but I won't because that is discriminatory to men and I should accept the risk"?
Put yourself in her shoes. I don't mean this metaphorically. Put on women's clothes, makeup, and order an uber. In the time it takes for it to arrive, notice the thoughts that appear in your mind and get back to me.