"As for why people disapprove of women dating outside their race - it is typically either a sense of ownership (in the case of racial puritans, who think they need to preserve their racial "purity") or people who perceive particular interracial relationships as unhealthy."

These are merely rationalizations each group uses to justify their opposition. Though the alt-right crowd is more honest in the sense that their espoused justification more closely aligns with the true driving motivation behind their disapproval for race mixing by white females. And IMO, this motivation is the underlying universal cause for all such thinking, regardless of racial or ethnic background.

It simply comes down to evolution and group competition, with every group competing against all others for their own group's interests. Of course sexual interests are arguably one of the most important, if not the only interest that counts (from a biological POV that is). Every human alive today is predominantly descended from ancestors who had high in-group loyalty and xenophobia. The human groups that did not possess such behaviors, were assimilated into groups that were at best, and completely genocided at worst. And from an evolutionary POV, males fucking out-group females usually means a successful conquest or subjugation (which could even be economic in nature, not necessarily militaristic) of said out-group; that then necessarily implies females breeding with out-group males en mass means your people have become conquered and/or subjugated. It shouldn't be difficult to see, which one of these outcomes is the more desirable option for one's group/tribe/clan.