The film certainly risks reproducing those classic, repetitive patterns of Western discursive authority over the Orientalized Other, tracing back to the Ancient and Medieval eras. After all, Spivak's famous line about colonial subordination, "white men saving brown women from brown men", occurs literally in the film and not as a metaphor.
But I also think the audience is repeatedly invited to entertain the utter ridiculousness of Orientalist stereotypes, like the assumption that the Orient is a "mythical" or "spiritually enlightened" geography where the damaged Western subject can go in order to be repaired. We see that, actually, these three brothers use the facade of India's "spirituality" as another way to do things like get high, have sex, and take pleasure in their tourism. In a cunning way, I think Anderson is, at the same time that he's exploiting Orientalist stereotypes, acknowledging and criticizing how the Western subject builds a fallacious and fetishized image of the Orient. In that way, the film sits squarely within the many paradoxes produced by the Orient/West dyad while also problematizing them. That opacity, I think, aligns with what is so perplexing to me about Orientalism.
Also, insofar as the Orientalist gaze is a projection of oneself onto the Orient in the psychoanalytic sense, I wonder whether there's a way to think about how each brother's inner life is projected onto Indian culture and society, shaping their understanding of the Orientalized Other. Perhaps Francis' insistence on achieving "spiritual enlightenment", his lack of a maternal figure, or the grief he feels from his father's death becomes projected onto the Orient as the site to provide him with remedies and healing. The same could be said of Jack finding solace in Rita after he breaks up with his girlfriend. Or Peter's uncertain feelings about being a father. In that regard, they all might hope their "lack," as Lacan would say, is filled by the Orient in order to make themselves feel complete.
I don't think the film blames or vilifies these characters for seeking spiritual relief, though. It feels like they are imperfect, like every person that has ever existed, but the film seems to look to them with tenderness and sympathy. Their desire to find some form of remedy to their problems, exploiting various Orientalist stereotypes, is certainly shallow and perhaps even narcissistic, yet also echoes just a painfully human feeling of wanting to be relieved of uncertainties. In that sense, I feel like the film raises some interesting ideas about how we might think about spiritual tourism: can we take the emotional woundedness of the tourist seriously while also problematizing their course in their search for relief?