If someone is presenting themselves to you in person for entry into your bar, you have far more information to make a judgement on than the color of their skin... so it is not the same.
In the case of a woman coming into contact with some driver and volunteering location information like her home address, she has little to no information to make that judgement. Providing her just that bit of information, and allowing her to discriminate based on it, makes her safer. Ideally, she'd have way more information than just whether the driver is male or female. The reputation information helps, but isn't always reliable.
Are you saying it's not acceptable for a woman to choose a female driver over a male driver for a sense of her own safety?
Deep breath in... There are two types of discrimination. Paraphrasing Thomas Sowell, let's call them Type I and Type II.
Type II discrimination is the evil awful kind we rightfully rail against. It is "treating people negatively, based on arbitrary aversions or animosities to individuals of a particular race or sex..."
Type I discrimination is of the broader sort; "an ability to discern differences in the qualities of people and things, choosing accordingly." We run our lives with this kind of discrimination: is this food safe to eat? is this activity safe to participate in? do I trust this person given what I know about them?
>> Ideally, Discrimination I, applied to people, would mean judging each person as an individual, regardless of what group that person is part of. But here, as in other contexts, the ideal is seldom found among human beings in the real world, even among people who espouse that ideal. If you are walking at night down a lonely street, and see up ahead a shadowy figure in an alley, do you judge that person as an individual or do you cross the street and pass on the other side? The shadowy figure in the alley could turn out to be a kindly neighbor, out walking his dog. But, when making such decisions, a mistake on your part could be costly, up to and including costing you your life. [1]
This kind of discrimination is what we're talking about. I'd venture that not only is it OK, it is necessary. In this case, men that have had no background check, and whose form of employment is as an Uber driver are more likely to harass women (or do worse) than a female driver. Allowing women to make a selection based on this likelihood means that female customers that are alone can make choices to still use the service while reducing the overall risk.
Mitigation of this risk in normal taxi services take the form of background checks, bonds, and a chain of responsibility running from employer to employee to customer. It places more risk on the employer deliberately. Uber deliberately chooses to avoid this risk and responsibility. That choice is baked into their business model. That means enabling this kind of discrimination from their customers is a required feature of the service.
[1] Discrimination and Disparities, by Thomas Sowell
The real problem is that this is necessary.
This same thing that keeps on happening when we try to reinvent things "without all that stuff that just adds friction." As with software, one should understand the underlying reasons for constraints in the old system before building the second one.
Banking -> crypto and NFT "without all that stuff..." -> wash trading.
Taxi service -> Uber "without all that employer stuff..." -> drivers with no background checks and no interview process
I understand part of this is routing around the damage of monopoly maintenance (medallion system, for example), but let's fix that instead of taking away the protections in place.
Sorry for the rant. I know this is like asking water to run uphill.