Eorzea - and Hydaelyn as a whole - aren't particularly pleasant places to live in either. Especially when you consider the simple face that outside of settlements it's fairly easy for people to perish to all manner of horrible things ranging from the undead to bandits and everything else that qualifies as a threat. So interracial relationships are frowned upon very likely not because of something as simple as 'bigotry' and 'racism' but because there's a genuine risk of entire tribes, traditions and races dying out if sufficient levels of breeding aren't maintained.