Ancient Greeks and Romans did not think of themselves in the same way we use the modern term "white"
American neoracism is trying to flatten all of the world and all of history into racial categories that really don't even describe our country in this time very well, let alone all countries at all times.
What happened from the 17th century-20th century in the US was construction of racial categories, in the latter half of the 20th century there was a lot of effort to deconstruct these categories and their power over our thinking. Now, an attempt to reinforce and never let them go
There is a great book about the history of racialization in the US. I highly recommend it. https://www.penguinrandomhouse.com/books/233136/racecraft-by-karen-e-fields-and-barbara-j-fields/
Also highly recommend C. Vann Woodward's works, which were very important in informing the CRM. https://global.oup.com/ushe/product/the-strange-career-of-jim-crow-9780195146905?cc=us&lang=en&
In the long-term if we don't stop this stuff we will have the same kind of sectarianism as in places where they have ethnic civil wars. In the short-term, you're gonna get NYT pieces about how the Roman Empire was divided between whites, African Americans, Latinxs, and AAPIs.