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.
From my point of view you’ve just given an excellent argument against the philosophy that I will call, for lack of a better term, “beep-boop utilitarianism”. Allowing such a donation has an immediate, tangible and quantifiable benefit; but the norm you are eroding by doing so is much more valuable, and may be impossible to renegotiate if lost.
I’ve heard of “Short-term utilitarianism”, but I like yours better.