My general understanding of Ancient greece and Ancient Rome is that they didn't have the modern concept of race and cared more for their cultures and civilizations than for their genetic similarities.
But i came across this quote while arguing with another person: "Τὸ Ὅμαιμον, τὸ Ὁμόγλωσσον, τὸ Ὁμόθρησκον καὶ τὸ Ὁμότροπον" ----> "Same blood, same language, same religion, same lifestyle" from Herodotus apparently.
So this got me wondering if my previous assumptions were accurate.
Better to say that when the Greeks and Romans excluded, they had their own grounds and categorisations with which to exclude and other. More can always be said on the matter if anyone would like to toss in their knowledge; while we wait for new material, OP, this previous post by u/toldinstone goes into what the Greeks and Romans did exclude for.