I'm pretty sure these racial categories are American abstractions, whose names have only reflected their composition in recent decades. The Irish, for instance, were long not considered 'white'; they were just 'Irish'.

I live in the US, but was born and raised in France and Greeks are considered white there. If the 1998 football team described as "black-blanc-beur" had included players of Greek descent (and maybe it did?), they would have been part of the "blancs", just like Youri Djorkaeff.

Take what you read with a grain of salt. I'm certainly very skeptical of the implied claim that Germans wouldn't consider Greeks as white.

Note that being considered white doesn't preclude Greeks from being discriminated against, just like some people discriminate against e.g. white Poles.

Greeks, like Armenians in USA are kind of a tossup case, see for example the YA novel "The Westing Game" where a black character compares themselves to a Greek with darker skin

Depends on the place and the person, but some certainly are racist against Greeks.

The point is that Germans are not in the habit of classifying people by race unless they're racist, and even then they don't tend to think in terms of Whites vs Blacks. For Nazis, it's about Aryans vs Jews, where the "Aryan race" is considered to consist of tall, blond, blue-eyed people. Most Greeks would not be considered Aryan, as would most Germans, for that matter.

I find it quite telling that you are surprised Greeks might be considered anything but white, while not showing any surprise about Turks. I don't think there's any difference in skin color, so that confirms my suspicion that "whiteness" isn't just about looks.