the_dunk_tank

I don't know enough about Tibet to know whether the Air Tribe is offensive

I wouldn't say that it's offensive but it's definitely a heavily stereotyped representation of Tibetan Buddhism. I'd say it's benign racism, or the western gaze to be precise, more than anything.

but iirc Ba Sing Se is most analogous to the Qing dynasty trying to maintain its social hierarchies at the expense of being unable to defend against an invasion or provide for its citizens. The whole Earth Kingdom isn't like that, it's just the capital stronghold with the political elite. I think it distances itself from the racist brainwashing trope because it establishes political reasons for why it's like that and doesn't imply that its people are naturally obedient or uniquely propagandized.

Yeah, I get that it's about the Qing Dynasty (hence my reference to the Opium Wars) but it's not just the political elite which is brainwashed and the character Jet literally becomes a Manchurian Candidate in one of the episodes.

Honestly I think you're doing diagetical handwaving to excuse the use of the trope by using in-universe justifications for it. I don't think that it really matters that there's a rationale for the brainwashing within the story because it's literally resting on the well-worn ground of invoking the trope of brainwashing in reference to Asian cultures regardless of that fact.

That's a bit like having a fantasy African culture and establishing the centrality and necessity of having caricaturised witch doctors to the story and using that as a defence for the use of the caricature; it doesn't matter if "ooga-booga" literally represents something meaningful in that universe because outside of the narrative, in the real world, it's still a racist trope. The same goes for Tikki Tikki Tembo;that story has a diagetical rationale for the caricatures but it's still racist all the same.