I would think just having driver and passenger gender preference/restrictions in the Uber or Lyft app would work too. Don't really need separate services.
Why stop at gender? Why not race or religion? Also thank God that I could prefer a male driver, I mean, it's an automobile and I'm merely entrusting the driver with my life, right?
And if female drivers suffer from my misogyny, they can deal with it, right?
/s
I get why it's a prickly issue that US based companies might not want to wade into.