The Dornish are not PoC. They are "spicy" white people; even in today's society, the British/Western EU white people can be both xenophobic and racist towards Southern/Central white Europeans.
Rhaenys' mother, Elia, was "white" bc the Martells (yes, translated into modern racial identities) are "white". Rhaenys was "white" and Rhaegar certainly wasn't any sort of PoC or PoC adjacent.
In her world, Rhaenys was just not the "right kind" of "Westerosi"/"white" that we'd also consider to be "white". Which is pre-extensive slave trade England-France-Germany--NorthWestern Europe pale people--in our specific matrix of global racial systems.
Which also doesn't include her own father; he is not shown to be xenophobic towards Dornish people.
Her maternal lineage/ethnicity.
So really, she did not have the "right kind" of lineage even as these people didn't actually think of her as "Dornish" bc she was born into the Targaryen royal family...just a "Dornish person's child". Any child born into the Westerosi royal family is not considered "Dornish", northerner, etc. They are considered part of the nonDornish Westerosi family, but with a different lineage. Remember Larra Rogare (mother to Aegon IV, Queen Naerys and Aemon the Dragon Knight), how non-Dornish Westerosi were xenophobic towards her and her brothers despite the fact that she was pale skinned/pale-haired AND had Valyrian roots/lineage? Because she refused to speak the Common tongue, kept to herself and her Essosi/Lyseni ladies-in-waiting, and worshipped various Essosi gods instead of adopting the Seven?
At the same time, there was the idea that people who worshipped different gods or/and looked as if they came from an area associated with such "foreign" types of worship or speak the same language a particular "native" way or eat similar enough sorts of food (i.e., Rhoynar are Essosi and Essosi don't worship the Seven near-ubiquitously like and Dornish people eat much more spicy foods), xenophobia can overlap with racism or really lead into it. As it would have done if Daeron I had been successful in conquering Dorne. That is how racism originated, btw--religion & class distinctions and not necessarily skin by itself.
It'd be more accurate to say Rhaenys is a mixed-lineage child.
I raise these maps bc I want to make it clear that Dorne is not that populous compared to other realms; only a few people live in the Red Mountains, the southern deserts, and the Greenblood river valley. As you can see, the major castles and most people live near or on the few rivers
This is the description of Dorne in terms of cities in AWoIaF -- "Dorne":
There are no cities in Dorne, though the so-called shadow city that clings to the walls of Sunspear is large enough to be counted as a town (a town built of mud and straw, it must be admitted). Larger and more populous, the Planky Town at the mouth of the river Greenblood is mayhaps the nearest thing the Dornish have to a true city, though a city with planks instead of streets, where the houses and halls and shops are made from poleboats, barges, and merchant ships, lashed together with hempen rope and floating on the tide.
The Red Mountains that compose its western and northern boundaries have kept Dorne separate from the rest of the realm for thousands of years, though the deserts have played a role as well. Behind that wall of mountains, more than three-quarters of the land is an arid wasteland. Nor is the long southern coast of Dorne more hospitable, being for the most part a snarl of reefs and rocks, with few protected anchorages. Those ships that do put ashore there, whether by choice or chance, find little to sustain them; there are no forests along the coast to provide timber for repairs, a scarcity of game, few farms, and fewer villages where provisions might be obtained. Even freshwater is hard to come by, and the seas south of Dorne are rife with whirlpools and infested with sharks and kraken.
For more reading, you may look at 🔗this essay [excerpt]:
In the mountains, access to rivers and rainfall raised the Daynes and the Yronwoods to kingship - although clearly trade was equally an important factor, given the rise of the Fowlers who claimed no such water access but who dominated the Wide Way that is the major caravan route in and out of Dorne. In the southern deserts, water was so important that the political class were called "the lords of the wells," although technically the Drylands and Ullers were/are riverine rather than oasitic. The Greenblood gives us the best example of how geography and culture interact: here, the necessities of cooperation to construct extensive irrigation works, which take larger labor forces than any one in-group could provide, as well as the common reliance on a single river (which requires some means of negotiating water rights between upstream and downstream), contributed to the creation of an elective High Kingship in that region.
Other aspects of geography can be shown to have shaped Dorne in other ways: the wind and water currents that cause the "big storms that formed down in the Summer Sea would pick up moisture moving north until they slammed into Cape Wrath. For some strange reason the storms never seemed to strike at Dorne, "which restricts agriculture to a few regions and leads to Dorne's "thinly peopled" status. The lack of accessible harbors along the southern coast of Dorne which restricts maritime commerce to the far east of Dorne (although I remain puzzled as to how merchants going from and to Lannisport or Oldtown do for water and other supplies).
So to that past anon who was all like "like climate and geography is not the same as culture", no it is not, but it definitely and always gives rise to the particular character of a culture as culture is basically humans' response to their environment.
This is the Greenblood, described as having "shallow" waters:
So we're trying to pin down whether the Martells AND Dorne are a PoC realm/people/etc, right? If we are talking about how "race" exists within the world itself, it is almost impossible to really transfer what we know as "race" onto characters from Dorne based on skin color alone bc their world is simply not like ours at the end of the day. The history & current conditions are not the same, even with it being similar in some ways I already described below to Spain's own history and the Welshmen's own histories.
I know that the comics may have Dornish characters that are "browner" than nonDornish Westerosi in skin color. But it is just a fact that GRRM made the Martells (as a unit/popilation/a people/a collective) and several "salty" Dornish to look more like European Southern and Mediterranean white people [look at the 2nd link above--that pic I showed of his blog answer to a specific question abt it]. Those white people that English and German people have thought of/racialized as the "spicy" whites bc their culture is a lot closer to the non white ME, North African, and other Asian influences throughout their own history and thus have had ME, North African, etc. influences in their own culture. It doesn't make those "white" EU territories any less "white" in our own many racial systems. But they are considered "lesser" whites, esp the darker they are.
Spain has a lot of Arabic architecture, the language is heavily influenced by Arabic bc of Ottoman, "Moor" (an exonym that encompassed several people: Arabs, Amazigh, and Muslim Europeans), and other non"white"EU peoples. There were "interracial"/interracial marriages here and there. There was the Umayyad conquest and the subsequent Muslim imperial control from 711–720s. You see all these influences in the foods and some other practices....it doesn't make Spain a non white country. Dorne is the fictional analogy of Spain (imperfectly, but closest of all we have) if Spain constantly fought to keep itself out of others' imperial rule, like the Welsh and Irish.
I actually say all this more or less HERE, & HERE too.
AND the population of what we call Dorne also has paler skinned non-Martells like the Daynes, the Fowlers, and the Yronwoods. All these houses have pale skinned, a range of eye colored, and blonde haired members from time to time. They are what Daeron I called "stony" Dornish; those who had the least Rhoynish "influence", but still have the accent and some Rhoynar ancestry.
In that post I linked all the way above, I also already gave the picture of Oberyn Martell GRRM had referenced made by Amok, one of the few artists he says represents many of the canonical physical features of his characters. Some of which he personally instructed Amok with detailed descriptions himself. And Oberyn has "olive" toned skin, but so do many Greek, Spanish, Portuegese people.
As for "sandy" Dornish people they tend to be much darker than either the exonymically named "salty" and "stony" peoples. Examples are the Ullers & the Qorgyles. They also existed before Nymeria came around and were First Men/Andal peoples then, like most other Dornish Houses I listed. They were "white" before her arrival. Some maybe married a few of her female warriors OR the children of those women and the Martell/other "half" Dornish people and thus you have a line of people stretching from before the Conquest who people would call "mixed" but that's like saying that Spain is full of mixed people bc of their own long past history of mixed marriages. The Dornish are uniquely themselves, or supposed to be:
LINK to So Spake Martin on Dornish Influences
Now why did the population per mile, or the "thinly-populated" detail matter? To paint a picture of how many people we can actually maybe say a "brown" racially vs "white", and thus from what we see here, Dornish people are mostly "white", and even the Ullers and Qorgyles, in our own world's racialization, is racially "ambiguous" (again, how U.S. and I assume England would racialize...GRRM is born-raised American writing to a mostly American audience and will likely be writing under the racial understanding of Americans). Therefore, it is a "spicy white" territory/state. And it is not like the U.S. that has a history a different race from somewhere else colonizing/enslaving the "native" populations and then down the line we still see differences b/t the Dornish populations where darker Dornish are put oppressed and deliberately segregated from paler people and yield a "nation" with several different ethnicities. Dorne is a territory with different Rhoynish influences-by-degree, and nearly all still worship the Seven like Andal nonDornishmen. Nearly all "forgot" the Rhoynar language but still speak the common tongue with a noticeable accent bc of that Rhoynish influence (I tend to imagine it like if a person were always speaking English with a Spaniard Spanish accent). Nearly all the houses practice absolute primogeniture, unless we go more north ("stony"), and even here it's told it's "some", not all.
In their world, racialization is just...not the same as ours (I'm talking U.S. and England) and even under the evaluation of race-translation, the Dornish are apparently more Spaniard/Portuegese white than South East Asian-East Asian-Mid Eastern, etc.
Even with Aerys making as if she "smells" like a Dornish person--NW Europeans often did the same to S and Medite Europeans towards renaissance and the early mod period. Sometimes continue to do so even today, and to Central Europeans like those from the Balkans.