Hi people!
I am a Hindu tarot reader (okay no, student) from India, and I don't see why anybody should have any hesitation. Actually Indians are just as curious about Tarot, as they are about I-ching or any "other" form of divination. To be honest, most Indians are majorly curious about their future, and love having their fortunes told. Which would sadly explain why all the charlatans, "babas" are such a hit. I am not saying there are no genuine fortune tellers, maybe there are.. I am just not aware of them. But you are right, Indians in the bigger cities are aware of the tarot, in the rural side, maybe it is numerology and kundali (horoscope) matching they are more aware of.
You don't have to project it as something "Western" if you think it might put your Indian sitters off. You can just tell them it is another form of divination, and give them bits and pieces about the origin (I am not suggesting you deceive them, just tell them enough to keep the mystery alive
) and you could add that there is an Indian tarot deck too, if you have that, just to let them know that although the Tarot does have christian origins, it is universally applicable. Oh, I am sure every Indian believes in God/Higher Power/Universe. So, basically what you are doing while reading is really meditating and putting your query OUT THERE, and letting the energies and the cards do the talking with their images, which you will interpret of course. That is what I tell my sitters. so, really what you are doing is kind of like meditating and introspection for an answer, albeit in a much mysterious, colorful and fun manner, that dates back to the 14th century probably (I could be wrong, I don't have a very strong grip on History of the Tarot)
As for worrying about Eastern and Western concepts, actually I find the whole Fool's Journey akin to the Eastern concept of achieving moksha, which could be shown in the World. It speaks of the four stages of Hinduism in a wider context, Brahmacharya (where the seeker goes off in pursuit of knowledge and thus the Fool begins his journey), Grihasthashrama (the seeker settles down and pays his dues in terms of material societal obligations like marriage, raising a family etc), Vanaprasthashrama (he exits the previous stage, and starts living like a Hermit), Sanyasa (he leaves everything behind in pursuit of a Higher Truth) and then finally achieves enlightenment, post Judgment in the World. at least that is my way of looking at stuff. If this is too complicated, one Eastern concept everybody is familiar with is Karma. Karma is totally represented in the Wheel of Fortune. What goes around, comes around. Like this, I am pretty sure several other correlations may come up if you look real close at the cards and try figuring out Eastern connections, but honestly I don't think it would bother the sitters that much.
Also, Tarot does not clash with our religious beliefs at all, just saying. Even if you were to show them the Death card, standard RWS which shows a person in papal attire kneeling before Death, who sits on his gleaming white horse, they might actually be interested in the background of the card and may not consider any card offensive unless you are reading with some erotic deck or deck that has got lots of nudity in it, which might offend them. even so, I think a good many Indians are okay with the sexuality in the tarot, so long as you explain it to them in the right way. You would have an interesting experience too, if they were able to bring in some additional astrological attribution to the cards, and that way you can explore two different systems together, and meld the two and give them a reading.
It is bound to be fun
Just go along with it, don't treat your Indian sitters any different from the rest (except unless, like previously mentioned..you read with some risque deck) because we all share the same concerns. Love, Work, Money, Family etc...
Just a tip: You could tell them the hierophant (if it pops up) is kind of a stand-in for our "guru" or God, apart from it depicting organized religion, rules and regulations, tried and tested etc... I am sure there are loads of interesting tidbits that you already know, anyway I just thought of sharing this