Indian gods and historical figures are usually depicted as fair, in their own, contemporary art.
That's because it's almost certainly true! it's why Indians speak Indo-European languages, and why the same Y-chromosome haplogroup (R1a) is common among (for example) Indian Brahmins and Norwegians.
> This theory is often connected with a view that fairer-skinned people represent "true" Indian culture
The Hindu religion in its most ancient form (see e.g. the Rig Veda) derives from the Proto-Indo-European religion, parts of which have been reconstructed: https://en.wikipedia.org/wiki/Proto-Indo-European_mythology
(Obviously modern India culture comes from a lot of other sources too!)
> including the Aryans who are said to have invaded India.
You phrase it that was as if to imply that it didn't happen. But I think the evidence that it did: linguistic, genetic, archeological, is very strong.
1 - https://en.wikipedia.org/wiki/Bactria%E2%80%93Margiana_Archa...
Actual Indo-Europeanists today eschew the label "Aryan invasion theory" in favour of e.g. “Aryan migration theory”. While genetic evidence makes a (limited) case for presence of force and population movement in the spread of the Indo-European languages to India, the bulk of the spread was through language shift whereby the indigenous inhabitants gradually adopted Indo-European languages as higher prestige.
Edit: i think i misread your comment, so there is no arguing with you actually.
If anything Augustus looks to be modern eastern european (from its famous statue).
What's not correct about "white" when depicting roman aristocracy? From all the statues we have they were certainly neither asians nor black nor from india nor descendants of, say, the aztecs.
Here's a reconstruction using AI of 30 roman emperors and I'd say 27 of them look totally white.
https://www.boredpanda.com/realistic-recreations-ancient-scu...
Heck, they even made Augustus with blond hairs and blue eyes (I have no idea if that's correct: all I can say his is marble statues looks like the modern easter european type to me).
Now I can understand they didn't sound british when speaking, but I don't see why you write "white, british actors". If anything, and there's nothing racist in there, "black british actors" would have been weird no!?
Or maybe you meant to say most of the aristocracy probably had the "mediterranean" type? (which I don't think is true and which, anyway, is classified under "white" I think?)
EDIT: TIL: Augustus' biographer, Suetonius, wrote that Augustus indeed had golden hair and clear eyes. This comes at a surprise to me.
I happened to read a relevant passage on this a few weeks ago by Erik Jensen in his book Barbarians in the Greek and Roman World. In explaining how ethnicity worked in the ancient world, he gives the example of how the Greek historian Herodutus argued that the Colchians of the Black Sea were of the same "ethnicity" as Egyptians. Whether or not there was a connection is a different question, but how it was argued is more interesting, since it reveals the mentality of the time. He dismisses arguments made based on skin-tone as a red-herring since people can have all different appearances and be part of different cultures, but instead focuses on language and cultural customs (notably circumcision). If we believe his account, then if Colchians were to time-travel to modern times, most of them might be considered "Black", despite that most people living in that region today would be considered "White" -- but they were considered neither at the time, they were just "Colchians" that (according to Herodotus) had moved from Egypt