Romans were pretty racist, too.
Would I be wrong in assuming that most nations of the Greek and Roman time periods were racist?
Actually most nations were more concerned with cultural superiority and ethnocentrism, which sometimes went hand-in-hand with racism but not always. This is true in the Mediterranean, which actually was far more of a melting pot than is now portrayed in Hollywood- some of the Roman troops to invade England, for example, were Africans- but I'm not so sure of other places. The Romans were more cultural imperialist than racist- if you spoke Latin, were educated the Roman way, worshiped Roman gods, and followed Roman laws and customs, you were a proper Roman regardless of what part of the empire you were from. If not, you were a barbarian (or at least foreign). There actually was at least one fairly popular black emperor (who was properly Roman), in contrast to a disliked Germanic one (who was not).