Romans didn't see race as a thing by the time the empire was created. Emperors were very multicultural. Aside from Septimius Severus who was from Africa (meaning, the Roman province of Africa in Carthage, not the whole continent), there was Maximinus Thrax from Thrace, Philip the Arab from Syria, Trajan from Iberia, and countless others who were not Roman or even Italian in origin.
During the Republic it was different, you had to be literally Roman to make it far in politics - not even Italian would do, because during the Republic, Roman citizenship was not given away unless you were born in Rome to parents born in Rome, or something. Citizenship laws were relaxed over the course of the empire, which was one of the causes for its eventual collapse in the west. They gave away citizenship to Germanic and Gothic tribes without first Romanizing them like they did previously, and then the Germans and Goths wrecked them once they were permitted to settle within Roman borders. You can tell for example that Africans (again, meaning people from the province of Africa, not the entire continent) were Romanized - the guy's name is Septimius Severus, he would have been born and raised speaking Latin, he would have honoured the Roman gods, he would have been educated in the Roman style, etc. For all intents and purposes, the guy was as good a Roman as anybody from Rome itself, even though his race was obviously different, and that was the Roman attitude to race. If you were Roman in upbringing, you were Roman full stop, doesn't matter about your skin colour. You didn't even have to speak Latin. The Eastern Roman Empire survived for nearly a thousand years after the Western Roman Empire collapsed, and they spoke Greek for the entirety of that period while still considering and calling themselves Romans.
like another poster said, romans were basically modern day Americans...any color or religion, as long as you was raised in American culture and speak the language you're considered American...
