You are correct, of course, that modern art tends to homogenously paint as white all figures from Ancient Greek and Roman history/mythology, unless they are to be explicitly marked as ‘not-Greek’, such as Memnon, king of the Ethiopians in the Epic Cycle (though he is in fact a more complicated figure than you might think). But there are potential difficulties in comparing modern artistic styles with ancient standards in this regard. Firstly, modern concepts of ‘race’ do not translate well into the ancient world, where skin colour was not a particularly important concept for classifying social in-groups and out-groups; instead, the most important qualities were shared language, shared customs, and ideally also shared descent. The dominance of Hellenistic cultures after Alexander’s conquests meant that many non-Greeks were incentivised to join this culture (i.e. ‘to Hellenise’ as an intransitive verb), and so we find the Phoenician city of Sidon honouring Diotimus, one of its citizens, for triumphing in the panhellenic Nemean Games in around 200 BC. These games were open only to Greeks; to justify Diotimus’ participation and victory, the honorary epigram composed by the city emphasises that both Cadmus and Europa were Phoenician, and that the Sidonians were, in a sense, therefore Greeks as well (and implicitly perhaps that the Greeks themselves were Phoenicians). As the example of Andromeda shows, the pan-Mediterranean nature of Greek mythology, stretching from the Straits of Gibraltar to India, allowed non-Greeks over a huge geographic space to Hellenise and define themselves as Greek, to whatever degree they wished.

Also complicating this is the fact that, while modern artists have depicted all the characters as white, so too did the ancient artists, as in a famous fresco from Pompeii (you can see a pic of it here https://www.joshobrouwers.com/articles/perseus-rescue-of-andromeda/ taken, I assume, by r/AskHistorian’s very own u/JoshoBrouwers). While the ancient Greeks might well have known that a normal woman from Nilotic Ethiopia would not have been white, Andromeda was not a normal woman from Nilotic Ethiopia. She and her family all have perfectly good Greek names (shared language), they share Greek customs (worshipping the same gods), and have shared descent (all related to Danaus, who was Perseus’ own ancestor). So despite being Ethiopians, they were also Greek, and as such are represented as Greek.

This apparent paradox was aided by the very ambiguous nature of the Ethiopians in early Greece. The Ethiopians were associated with the sun: the Greek word Αἰθίοψ (‘Ethiopian’) is derived from the verb αἴθω (‘to kindle, blaze’) and the noun ὤψ (‘face’). But two regions of the world are connected to the Sun: the south, where the sun is most intense, and the east, where the sun rises. Andromeda’s Ethiopians are typically located to the south, since Perseus encounters them on his way back across Africa; Memnon’s Ethiopians, however, are presumably from the east, since Memnon is child of the Dawn, who – like the sun – comes from the east. And just like with Andromeda, there is considerable uncertainty about Memnon’s skin colour: on some vases he is depicted with markedly different skin-colour to the other figures, but on many he is the same as the other Greek characters. His name is Greek, he worships the same gods as the Greeks, and he is the son of a Greek goddess (the Dawn) and a (pseudo-Greek) Trojan, Tithonus. Both he and Andromeda were simultaneously Greek and Ethiopian, and could switch between the two as necessary. Similarly, at some times the Egyptians are described by the Greeks as black (as in Aeschylus’ Danaid trilogy), and at others as similar to the Greeks; it depended on the interests and aims of the author/artist, and was fundamentally flexible and malleable. I suspect also that this ambiguity with the Egyptians may have been influenced by a deliberate or accidental misunderstanding of the Egyptian language: the typical Egyptian word for ‘Egypt’ at the time was kmy, etymologically (‘the Black Land’); the Egyptian for ‘an Egyptian’ (Coptic rmnkhme) would therefore have sounded very similar to the Egyptian for ‘a black man’ (Coptic rōmnkame).

This is not to say, of course, that Greeks and Romans (particularly later on) were not aware of the incongruities involved in this. Quintus of Smyrna, in his ~3rd century AD epic Posthomerica, makes use of Memnon’s traditionally ambiguous skin colour to repeatedly evoke ideas of light and darkness in Book 2 of his poem (in which Memnon appears), contrasting the hopeful light Memnon brings to the Trojans with the darkness of Achilles’ threat. This idea is more explicitly played with in Heliodorus’ Aethiopica (a 3rd-4th century AD novel): the two main characters are Theagenes and Charicleia, both paragons of Greek male and female beauty respectively. But in Book 4, we find out that Charicleia is in fact Ethiopian: her mother Persina (queen of Ethiopia) was having sex with her husband and at the same time looked at a wall-painting of Perseus bringing Andromeda down from the rock (exactly like the fresco I linked earlier); as a result, Charicleia was born white. The situation is obviously absurd: Persina is looking at a famously, incongruously white Ethiopian (who she furthermore claims is one of her ancestors), and this causes her to give birth to another incongruously white Ethiopian, who has to be abandoned so that Persina is not accused of adultery. Heliodorus implicitly asks the question you have asked (‘why was Andromeda white’) but supplies no answer himself, and so suggests that there is no logical reason for why the Ethiopian Andromeda is always painted white – she just is.

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