When we lived in Israel we had a Sephardic friend who was originally from Bombay. There was, and probably still is, a large community of normative Jews in India who for centuries did not accept the "bene Israel" as being authentically Jewish because they practiced some weird religion that combined bits and pieces of Judaism, Islam, Hinduism, Buddhism and whatnot.
I also had an Indian Hindu co-worker tell me that she thought she was Jewish.