I would say basically if the person is working on/with your body or if they have some form of physical power over you which is the case if you are getting in their car (and they could in theory lock you in/drive you somewhere else).

It is e.g. totally fine if a black person would prefer another black person as a hair stylist because they feel they know more about black hair. Same goes for a white person prefering a white hair stylist. At a certain point you should probably ask yourself if you can still participate in society if your demands get too detailed. I would draw the line where the interaction is very unpersonal and takes place in a public setting. Everybody can have a one-minute exchange with any chashier. But as soon as the employee is going to work on your body or put you in a position where you can’t easily leave it’s fair to choose who works with you.

I know a lot of people who have a gender preference when it comes to doctors. Not just gynecologists, but any. I know people who’d only go to a male or female massage therapist. I know asians who’d only go to an asian hairdresser. These are all choices people make every day, we just don’t notice because we don’t filter it through an app.

As for bigotted people, I don’t think you’ll change their mind by forcing them to interact with you. If I was e.g. a hindu driver I might even feel safer knowing that people who hate my religion can choose not to be in my car. The safety concern goes both ways.