I think there's some confusion but not sure which end its on.

First some terminology in here. In ancient Greek "barbarians" (ie βάρβαροι) just means "foreigner." Anyone who couldn't be considered Greek (Ελλενη) was a Barbarian. That includes Persians, Lydians, Celts, Syrians, Phoenicians, etc, and even Romans or Macedonians at earlier points. In Biblical Hebrew "goy" (גוי‎) just means "nation" and is used to refer to both the Hebrew kingdoms and foreign peoples. The modern use of "goyim" for "non-jews" is actually a product of Yiddish [See AksiBashi below]. However, you are correct that the ancient Jews/Israelites/Hebrews saw themselves as religiously set apart by the return from Babylon at the very latest.

This is where I get a little confused. To the ancient Greeks, everyone esle (Jews included) were barbarians. To the Jews, everyone else (Greeks included) were goyim in the Yiddish sense. Thus most of the world falls into the category of "barbarian goyim." To the Jews, they were all still just goyim and to the Greeks they were all still barbarians.

Are you asking what Babylonians, Persians, etc believed about foreign gods or what the two cultures in your question believed about those cultures?