Romans did not have any kind of racial theory like European colonizers of the early-modern age did, and did not seem to have been hung up on skin colour at all.

That is not to say they did not discriminate or have stereotypes about other cultures: "Punic" Carthaginians were untrustworthy liars, Celts and Germans were savage, uncultured drunkards, Greeks were effeminate sophists, etc. Oh, and a lot of "kids these days don't have a proper work ethic, everything used to be better in the good old days." But at the same time, the Romans greatly admired Greek culture, and prided themselves on adapting good ideas and inventions of other peoples wherever they encountered them.

Egypt was, if anything, an exception to the rule in that Romans were particularly disdainful of native Egyptians and their culture, in part because of Augustus' anti-Cleopatran and Anthonian propaganda offensive. This led to a particularly oppressive form of Roman rule, with heavy tax-burdens and codified inferior status for the masses. (It should be noted that this had already started under the Ptolemies. Towards the end of their rule, the lines between Greek/Macedonian and Egyptian were starting to blur a bit, but the Romans solidified them again and put themselves on the highest rung.)

In his "Life in Egypt under Roman Rule," Naphtali Lewis writes:

"When heterogeneous populations are lumped together in a single political or judicial category, they are usually quick to create their own social gradations within the total group. In recent history such distinctions have often been based on skin pigmentation, as in India and in the Caribbean area. For the mass of Egyptians under Roman rule, the touchstone of status was Hellenism."

He goes on to explain how native Egyptians intermarried with descendants of Greek settlers, and would try to change their name (and thus status) to a Greek one, and how the Roman government threw up all kinds of obstacles to make this difficult.

We also have some rather oppressive laws on this that were preserved on papyrus rolls. There's a long list of fines and punishments for people who falsely claim a status which they are not privy to. For example:

"If Egyptians after a father's death record their father as a Roman, a fourth [of their estate] is confiscated."

"If an Egyptian registers a son as an ephebe [of a polis], a sixth is confiscated."

"Freedmen of Alexandria may not marry Egyptian women."

Lewis calls this "A veritable ancient apartheid."

Again, this does not seem to have happened elsewhere in the Roman empire. Though it should also be noted that we simply have far fewer records of other places, because huge quantities of papyrus documentation were preserved only in Egypt. Still, it's clear that Egypt's legal and political status was exceptional.