The differences between groups in the former Yugoslavia have little to do with race (as most Americans would understand the term). It's tough to tell the difference between a Croat and a Serb just by looking at them. Conflicts were based more on culture, religion, language, and perhaps something akin to "tribal" identity (not literally tribes but I don't know how else to describe it). Some of these conflicts date back to the 14th century.

The only significant group in the region which some might identify as a distinct "race" are the Roma. That minority lives in all of the countries and they didn't cause countries to split up.