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.
In practical terms it’s very normal for people to only donate a kidney because they have a specific recipient in mind.
Trying to say no, “you can not donate your kidney only to your son, you have to make the kidney available to everyone” does not make sense.
If you are running an anonymous donation facility then practicality comes into play. How realistic is it to keep tabs on all kinds of weird preferences? Matches are already hard enough. And how do you disclose responsibly?
From an ethical point of view you need to look at the big picture. It is not enough to say that this is a kidney that someone will get but would not if you don’t allow discrimination. You have to also think about whether such a policy will encourage people specifying who otherwise wouldn’t. And then a growing imbalance in recipients.