it should be noted that the concept of race (and especially of “whiteness”) didn’t exist back then

Or rather, it did, sort of, but it had very different baggage than it has now. The ancient Greeks knew about Ethiopians, and described their physical appearance. They also distinguished Greeks from one another by hair color and skin tone: Achilles was blond (or maybe red-haired-- classical Greek color terms are unclear); Odysseus dark-skinned (for a Greek). “White-armed” (famously applied to Helen) was a desirable womanly attribute, more because it implied the woman wasn’t doing work outside in the sun. But we don’t know if “white” meant like milk, or just not tanned as much as a peasant.

Hell, even plenty of Turks call themselves white these days

Turkey’s unusual, since the urbanites are mainly Mediterranean-looking, but some of the peasants from the hinterland look lighter-skinned and sometimes blond and blue-eyed.

If you look at old paintings, the orginal generation of Turkish invaders looked very much like Mongols (there are quite a few portraits-- the Turks back then were Muslim but didn’t observe the modern prohibition on making pictures of people-- the Sultans liked to hire Venetian portrait painters). Since then, they’re intermarried with the locals to such an extent that their appearance is just like the pre-Ottoman-invasion population of Asia Minor.