Rome was a very heterogeneous place prior to and during its height. There was a very variational core East Mediterranean component that was more MENA-shifted than today which would eliminate them in being classified as "White" in the strictest sense. Etruscans were not even Italic in language, Pompeiians were Italics that experienced the same broad interactions with the MENA world the rest of Romans had, so they were not an exception at all. We have people deep in Serbia from the Danubian sample set that illustrated how every Roman region had considerable heterogeneity.
Secondly, the people of higher MENA origin were mixed and would usually be the wealthy ones and be Romans just as the ones with higher Italic ancestry. Remember, Rome expanded and absorbed and acculturated other peoples in the Italian mainland who were not even Roman themselves in the beginning, i.e., these Pompeii samples are as Roman as any East med profiled anywhere outside where Rome expanded which was basically the majority of Italy. The non-Latin Italic tribes were not more Romans than those Pompeiians who I must remind you are basically locals that mixed over time and had stronger cultural ties to Romans even before the domination. A crucial component is to recognize Pompeii at the time was Roman.
The notion that so-called core people were true Romans and brown people were low class is not correct. Roman identity did not follow the modern conception of ethnicity - that is why it was so diverse in the first place. Usually, those brown people were buried in wealthy places with strong Roman cultural traditions. What you see on TV where White people rule, where slaves, servants, and lower-class people are brown and black is nonsense. Every Roman elite burial we have gotten study from has shown them to be highly mixed and none of them were on average "White."
Lets for the sake of argument say the core was Italic (which it was not. It was a diversified East Med but in a sub-populational sense that was very much not White. The coherency of the demographic was too complex back then compared to Italy today which is very phased, stabilized, and gradient-based). Those people were of low Steppe ancestry and would probably look like people of Turkey today or Caucasus because they lacked the enriched ancestry that we associate with the beginning of White people. It would be like saying "Armenians fit the strictest sense of White" when we know they don't unless it is some loose category that encapsulates major parts of the Near East of people with distinct backgrounds removed from the Germano-Slavic sphere.
My statement still stands, a racist white today who identifies with Rome as a White European civilization would not even accept the average Roman as his kin. Racists apply the strictest sense of White, even when they don't fit into it themselves. Rome was indeed whiter (notice how I don't say they were White-proper) in its first establishment, but it became heterogeneous and then more and more relevant across the board. There is a reason why identity became loose and wealth distributed very diversified throughout and not specially preserved for people with less mixture. The irony is, that the initial non-Romans of the Italian outskirt regions would have a bigger East Mediterranean component but they were not even Roman, to begin with, similar to Pompeiians. Rome proper was highly mixed and they were the culture bearers and transformers. The definition of what was a Roman also changed several times and during the Pompeiian samples era, would have been Roman in every sense. Nationality and ethnicity as you frame them now were an obsolete concept at that time.
Even their legionaries were of diverse roots if i remember correctly. There emperors as well at times.
I heard someone compared the Roman identity to the modern American identity, do you think that's accurate?
Even the foundational slave-economy part is similar if you even deep it.