We know the Roman empire was racially diverse, the Egyptians had Negro and red-haired Pharaohs. If you read the writings of ancient peoples, "race" is rarely mentioned, and I don't recall of ever reading about racial conflict of any kind. I don't think it was because race didn't exist, it's because it didn't matter.

In Classical times, nation fought against nation, and within a nation (an ethnic culture, actually), there were tribal, class and family conflicts. But in my opinion, racial prejudice may very well be a relatively recent invention.

I believe it started in the Christian era. Christianity was the first major, widespread movement that preached all men were equal. Slavery violated its very philosophical foundations. Of course, what you say is not always what you do, and old habits, particularly those with economic consequences, die hard. But by the time of the European expansion, it became harder and harder to justify the fabulously lucrative slave trade in the Indies with Catholicism. Only by considering the Indian, and the Negro, as sub-human, as not really people, could they justify it to themselves.

Different races have always had some conflict, and consideed each other barbarians. But I believe that is because racial geography often coincided with political and cultural boundaries. Consider Moorish Spain in the late middle ages. The Moors were black, although the Arab civilization they were a part of was racially diverse, with many Caucasian and Semitic racial elements. Spanish Muslims had a highly advanced and tolerant civilization. Cities like Granada and Cordoba had universities, libraries, civil courts, trade with foreign lands. That's where you went to study, or to get your teeth fixed. Christians and Jews were allowed to live there in peace, with guaranteed rights and legal protection. They considered their fair-skinned, Christian neighbors in Castile and France as little better than savages.