Not sure if I'm allowed to post a top level comment that's not an answer. I can't speak for Anatolia specifically. But in the ancient world, skin discrimination was generally not a thing. Instead culture, language, and religion were the primary methods of identification and conflict. The Greeks believed most other cultures to be barbarians, regardless of appearance. Germanic tribes, Persians, Egyptians, Romans, Scythians, they were all seen as inferior to the Greeks.

Knowing the skin tones of Ancient people in the Mediterranean, North Africa and what we think of as the "Middle East" is actually pretty difficult. There were a lot of migrations between then and now. The Germans took over a lot of Italy and went into North Africa and Spain for awhile. The mostly Arab caliphate conquered large swaths of land through out North Africa, into Europe, and as far as India. The Arab slave trade brought people into more contact with sub-Saharan Africans. Going back before all of that there was a lot of trade and intermixing of people through out the Greek and Roman ages And there were dozens of other invasions and such. For example, we have little idea what a "typical" Phoenician or Carthaginian looked like or even if there was such a thing as a typical look. All of that had their impact on how people from those areas look today.

We have a good idea of what the "typical" Greek or Roman looked like as far as skin tone. From descriptions of individuals and existing paintings. But even that is flawed especially dependent on the time period. There have been hypothesizes that a few different Roman emperors were not "white". Whether or not that's true, and I'm not suggesting it is true, it highlights how little we know about how these people looked at any given time.

As an example, St. Nicholas was born in Anatolia somewhere around 270 CE (you didn't specify time periods). Many (but not all) existing pictures of him depict him with dark skin. However, these are later depictions. Regardless of skin tone, he was unquestionably considered to be a Greek living with in the Roman Empire. Not something other than Greek or a second class Greek (he was from a good merchant family).

Greeks and later Romans did not think of people based on their skin color. If a skin tone was somehow outside of a norm they were accustomed to (and they would be used to a range) then it would likely be remarked upon or mark that person out as a foreigner. But even that isn't so sure in some more cosmopolitan city-states or later Rome where they'd see all types of people everyday.

Greeks and later Romans judged people based on what we would consider culture. Their concept of race would be more akin to our concept of culture and ethnicity. The story that the word barbarian comes from the Greeks thinking anyone who didn't speak Greek sounded like "bar bar bar" sums up the worldview. Having Greek as a native language, sharing Greek culture (know your Homer), and a link to a city-state (even if tethered) is what made one Greek. Everyone else were barbarians.

Roman outlook was different only insofar it was generally easier to become a Roman than to become a Greek (although standards would differ based on city-state). It would be very difficult to ever become a citizen of Athens, for example. But Romans often made their freed slaves or the children of their freed slaves citizens. A people who they had conquered and had since completely adopted the Roman way of life could be granted citizenship. And members of that culture could then enter the Senate or Equestrian class. There would be some grumbling about it but it was done frequently. This was as true of North African or Near East provinces as any others. To be Roman was to be part of a culture and to speak a common language (Latin, then Latin and Greek, then Greek). It wasn't a skin color.

Now both Greeks and Romans did have culture specific prejudices, stereotypes, and biases. The Romans saw the Greeks as intelligent and good tutors or doctors but effeminate and weak. They once saw the Gauls as inherently barbaric and warlike but over time, once Gaul was pacified, those fears transferred to the Germans and Gauls were seen as civilized and some of them considered Roman. But, again, that wasn't based on skin color.

They had the concept of us v. them but it wasn't primarily linked to skin color and was fairly fluid. Our modern concepts of race are relatively recent.