An extreme version of this is: What should the German health service do if someone says they are willing to donate a kidney as long as it doesn’t go to a Jew?
On the one hand, nobody is forced to donate a kidney and by forbidding this we’re making things worse for an innocent patient. On the other hand, it can be seen as the state sanctioning this kind of discrimination.
The question here is about a voluntary kidney donation from a living patient.
What conditions are you imagining in which a donor is living but not aware of specifically who would be receiving the organ before agreeing? Tests need to be done to ensure compatibility, and a kidney is a lot to ask and probably wouldn’t be agreed to unless it helps a loved one.
I feel like this is a strange premise whose goal is trying to try to move the line little by little until people are willing to say they’re a little bit racist/sexist. Or until people are willing to admit they don’t think others should have control over decisions made about their bodies. Be honest about your ends here instead of dreaming up fictions that make so little sense the answers are unproductive.