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There are stories of incest in the past among nobilities. You can search some of European countries who have a long history of monarch system. They have weird thinking of wanting to preserve their "pure" bloodlines so they marry each other's relatives. That's also the reason why they die early or have physical/biological defects because their genes are so fucked up.
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Inbreeding strengthens any kind of genetic traits, the good and the bad ones. So it is often used in animal breeding, for example, to have your cows produce even more milk, or if you want to create a new breed of dogs, and so on ...
Red eyes are extremely rare (only albinos have red eyes) and were often associated with being possessed by the devil or demons.
So I think, the authors simply use red eyes as a visible sign, for being something "special" and inbreeding to keep this within your family.
Isn’t this race of dark-haired, red-eyed people (gifted, but the product of incest) exactly like in Lucia? Is this concept actually rooted in some mythology/history or is it just a trope authors are copying?