Race can be a trickey issue . Putting aside how one does one precisely genetically define race, unless a group have been living on some isolated island or jungle somewhere for thousands of years no one is racially pure. Many geneticists argue it is a social construction. Consider the case of Obama, he’s typically called black but he’s half white. Under the surface, mixing happened. We should never confuse our identities with meaning we are racially pure. This is why so many leftists humanities types argue all identities are social constructions (which fits in perfectly with their antinationalism worldview)
Claiming modern Greeks are not “real” Greeks is practically an international sport today (sort of like antisemite sorts like to claim you are Khazars). I like to confront arguments not hide from them. I don’t know of a single ancestor in my family line that was non-Greek going back all the way back to the Greek revolution when government records were first officially started.
Although there are have been invasions of other groups into Greece too, Greeks (or Roman Greek speakers) have historically dominated the region. Despite this, presumably between myself and ancient Greeks some of my ancestors mixed with non-Greeks. It’s lost to time because of assimilation but it would be naive to believe none of my personal ancestors’ mixed for over 2000 years. Heck it would be naive to believe ancient Greeks themselves were racially pure anything.
This does not mean I am not directly biologically related to ancient Greeks (which can be checked with modern DNA testing) Or that my identity isn’t Greek. If I found out I was 5 percent Turkish, 5 percent regional Slav, 5 percent Albanian, etc.. my identity would still be 100 percent Greek.
Where I think some go to the opposite extreme of completely dismissing biology (typically lefists).. what does 5 percent Turkish, Albanian, Slavic, etc.. mean? Our neigbours have mixed with neighbours too! They are partially Greek origin (backed up with genetic testing). It’s the flow of history that matters.
This is why if I moved to China it would be silly to claim I’m ethnic Chinese. Now if I married a Chinese women and our kids were brought up with Chinese culture, they could claim to be Chinese even if of mixed heritage. And after a few generations of further mixing with local Chinese, the issue of mixing and assimilation would be lost to time. Their descendants would be 100 percent Chinese. That’s how nationalism works.