Women aren't allowed to drive in, e.g. Saudi Arabia, because they aren't allowed to be out of their home without a blood relative or husband. That could lead to mingling with the opposite sex or something like that. “What would happen if a woman got in a car accident? Then she would be forced to deal with the male driver of the other car, a stranger, with no oversight." [0]

So I don't think self driving cars will solve that problem at all, sadly.

[0]: http://www.theatlantic.com/international/archive/2013/10/-ne...

Quora answers from people that appear to be saudi: https://www.quora.com/Why-are-women-not-allowed-to-drive-in-...