Were there any notable people of Mixed Origins in the Roman Empire? such as an Emperor?
If Anthony and Cleopatra had a Child, how would their half Roman half Egyptian/Macedonian Child be treated in upper class roman society?
One thing's for sure, our ideas of race are slightly different than theirs.
Next it depends on the time period, at the time of Caesar Roman elites tended to look down upon families from the areas around Rome. Gaius Marius faced some discrimination for the fact that he was a central Italian rather than a Roman of Rome itself. At the time ethnicity was very important and there was resistance to admitting Italian or Gaullish elites into the political system, illustrated by wen Augustus granted citizenship to Gaullish chieftains
By the end of the Julio-Claudian dynasty the definition of Roman citizenship had changed to almost any individual who spoke Latin and lived within the empire, though this didnt mean voting rights in the now purely ceremonial senate.
As the old aristocratic families went extinct the racial or ethnic importance evaporate too. Countless Emperors were of mixed ethnicity and born in many parts of the empire. There were African, Balkanic, 'Spanish', Arab, and Gaullish Emperors. The Roman identity by that point was a bit like French nationality today, it was psychological and ideological rather than ethnic.