The dilemma that I discussed in the OP broke down into these three options:
- Should we strip the cultural context from the borrowed monsters to avoid them becoming stand-ins for those cultures in worlds that don't already have stand-ins for them. (Like Eberron, which doesn't have a humanoid cultural stand-in for Middle Eastern people, but does have a nation of Rakshasa that wear similar outfits, have similar architecture, the same titles, etc.) This has the issue of possibly being mis-appropriation of those cultures' creatures.
- Should we just not use those creatures in the first place if there is a risk of them being taken as stand-ins for that real-world culture? (Again, would it better to just not use Rakshasas in Eberron as a major population of an area of the main continent and instead just use a different type of fiend to get across the same theme without appearing to misuse the monsters.)
- Should we instead include a humanoid version of the cultural stand-ins (like Al-Qadim) so there would then be a place for the creatures from those real-world cultures in the used setting? (Maybe by adding a Middle-East stand in to the area of the Demon Wastes or perhaps Sarlona/Xen'Drik to explain why they have similar cultures to the real world counterparts of them.)
A few folks have mentioned other creatures to consider, like vampires and medusa. To some of us, it feels like we can treat them differently than djinn and rakshasa. That might be worth exploring.
Vampires have prevalent pop-culture representation that has severed the creature from its European culture of origin. We're used to seeing vampires outside of Europe, and most pop-culture vampires still inhabit pseudo-Earth, which has a Europe, so when we do see a vamp with European trappings, it's not jarring. D&D has Barovia, sure, but most vampires in D&D adventures are creatures of whatever fantasy culture they inhabit.
Medusas were divorced from Ancient Greek culture from their introduction into D&D. Movie representations of Medusa are usually set in Mythic Greece (or modern-day expansions of Greek myth, like the Percy Jackson stories). But medusa don't appear in D&D in Greek settings or with Greek props or clothing, as far as I know. (Does Forgotten Realms have a Greek Counterpart Culture? I don't know.) Recent appearances in published books (ToA, PotA) put the medusas squarely into non-Greek fantasy cultures.
Djinni have been treated differently, and I think that leads me to consider them differently. First, djinn in pop-culture generally are always presented as part of an Arabic or Mythic Arabic culture. We don't see djinni adapted to other cultures. Or, I should say, I haven't seen it. Second, djinn in D&D have from the start (or at least since AD&D 1e) been specifically described as having themselves an Arabic culture. For that reason, having djinni appear with Mythic Arabian culture in a game world that doesn't have an Arabian Counterpart Culture feels ... questionable. In my experience, they've been coded as "not-mine" in a way that vampires and medusas have not, and that makes me want to be careful when I pick them up to play with them. (Not that I'm always careful. I haven't really thought about djinni much before this thread began, so it's been an opportunity.)
It could be interesting to remove the traditional culture trappings and see djinni as part of another culture, like we might see a vampire private eye in LA or an aristocratic medusa in Cormyr.
If the game world does not have a human Arabian Counterpart Culture, I wouldn't use djinni and leave them seeped in that culture.
If the game world does have such a culture, one might explain in a few different ways why the djinni's culture mirrors it. Perhaps, as one poster earlier suggested, the djinni adapt their appearances to the expectations of those they interact with. Or perhaps the humans mimic the djinni's social structure. Or perhaps the djinni emulate the human's culture for their own reasons.
Not sure if any of this is useful to the original poster or to the community, but there it is.