Do none of you find it just slightly disturbing how okay we all seem to be with this?
I, for one, oppose the idea, albeit on a purely biased and non-objective basis.
Sure, it's got the whole 'Realism' thing going for it... But even that's half-assed in this regard. Coming from a purely objective, game-play-related standpoint here, I have a couple ideas on the subject.
First off, give players a disincentive to inbreed. Inbred children should have a trait. First option to this end would be the trait 'Inbred,' which gives penalty(s) of some kind. Exactly what, I can't say, nor do I want to even try. Usually I'm all for examples and stuff, but I just spent a little over 9 hours finishing the current portion of my fan-fic and can't be bothered to think much harder than that.
Anyway, back on topic here... Second way to do this would be to give Inbred children a trait, but NOT the 'Inbred' Trait. ElanaAhova alluded to Inbred Royals having Hemophilia. Give the kid a trait like that. You could include any amount of traits, drawn from the wide variety of well-known side-effects of inbreeding. Hemophilia itself could be one of them, and an (easy) example of what it would do is, "Damage taken takes N times as long to heal." I can't say I'm exactly familiar with any of those oh-so-well-known side-effects so I can't give any more examples, but now you've got a jumping-off point.
Second, alongside either implementation of first idea... Give an incentive to Inbreeding. First, we'd need to change the 'Royalty' Heroes so we could instead give it to inbred kids. Or, just give another trait that has the potential of making inbred kids worthwhile, whatever seems best here.
But I digress... NO MORE VIDEO GAME INCEST! =P