Earlier quoted context omitted.
We can't conclude that the donor had an egg allergy. The immune system is complicated as hell, it could be the case that he had some weird protein circulating on his blood that was recognized by her immune system, and by chance this protein was structurally close enough to some egg protein that now eggs trigger an immune response on her.
"The immune system is complicated as hell." You got that right! My wife used to eat a banana every day. Then something in her flipped and she reacts as if she is allergic to bananas and the rest of the world - not exaggerating. She can eat a very small number of foods and has to avoid most people because of smells. It isn't allergies it is - you guessed it - her immune system. If we could just flip it back to "normal…
Little did I know, having postviral sequelae causes my immune system to start hating many things I used to eat. A food blood sensitive test showed that bananas, beef, coffee were what set my immune system off the most.
I was told it was gut permeability causing food particles to leak into the blood stream causing the immune response. So the fix has been to stop eating those, let the gut heal, and over time I've been able to eat those foods in moderation years later.