Does your job involve being alone with strangers in a situation where you control their environment? Cabs, car shares, etc. are a somewhat special situation as they routinely deal with people who aren't familiar with the area, operate at times without many witnesses around, and often get people who are at higher risk (drunk, sick, physically impaired, etc.), and they control the route, ability to leave the vehicle, etc.
It's not quite as bad as, say, child care but requiring stricter background checks really doesn't seem like an unreasonable expectation.
I've never had a job ask me if I've been convicted of sexual assault, and if anyone was going to be asked, you would think it would be someone with the last name Dildonics.