Well, a non-Ethiopian African playing an Ethiopian would be rather like the already-uncontroversial practice of casting English actors as virtually every figure from Antiquity, so it's hard to paint that as hypocrisy.
But, you're not entirely wrong. However, I don't think that this necessarily reflects sloppy thinking, or at least not sloppy thinking. The drawing of the "diversity" line between "White" and "not-White" was not drawn by those calling for more diverse casting, it was drawn generations ago by those making casting decisions. Studios have historically biased casting towards people of Northern European origin, not out of respect for historical authenticity, but because audiences, specifically American audiences, are assumed to more readily identify with people of that origin.
For example, in stories with Greek protagonists, casting is predominantly Northern Europe. Gerard Butler is Leonidas, Collin Farrell as Alexander, and so on, because apart from the obvious concerns surrounding a billable lead, this is understood by American audiences as a short-hand for "Us". But when we want the Greeks to appear exotic, when we want to clearly signal to the audience that they are not-Us, we are free to cast actual Mediterraneans. For example, in the last season of
Vikings, our impeccably Aryan heroes travel to Byzantine Sicily, where they meet a Byzantine governor played by a Portuguese actor, and an Abbess played by an Anglo-Moroccan actress. Greeks are permitted "authentic" complexions only when that complexion is a shorthand for the exotic and the Oriental. (I imagine that
@Kyriakos can furnish us with more examples- his contempt for Hollywood mishandling of Greek history has been noted.) So it's clearly not enough to say that studios simply make too many films set in Europe when the same racialised coding appears in period pieces set in Europe.
At any rate, consider that they set
Exodus: Gods and Kings and
Gods of Egypt in Egypt, and
Noah in the Levant, and they still cast a bunch of Brits and Ozzies to play Egyptians and Levantines. There are few exceptions to this "Western Civilisation Is Very White" rule; the only one that leaps to mind is
Hercules, which cast an Afro-Samoan as the titular character, but then filled out the rest of the cast with Brits and Norwegians. (And I don't know how much credit it gets when the film was mostly a vehicle for said Afro-Samoan lead.) The enduring problem is that studios assume audiences will only see films set somewhere in the march of "Western Civilisation", and that membership of "Western Civilisation" must be clearly shorthanded by peely-wally Nordic faces.
So, the push-back tends to follow an uncoordinated call for non-Nordic faces because that is the barrier which exists. People don't spend too much time fretting over the historical nuances because so long as this subtle, informal racial barrier exists, historical nuance isn't really on the table. If breaking down that barrier means a few bizarre casting choices, if it means the occasional black Achilles or, I don't know, Puero Rican Charlemagne, that's not a terrible price to pay for a century of Aryan Israelites.