So far as I can recall, from I my studies of anthropology a half century or so ago, back when Dr. B was still (figuratively, anyway) in short pants, the definitions of religion I saw didn't line up with his. The salient points, if I recall, were that religion was a social activity, involved supernatural beings or other sacred objects of veneration (ancestors, mountains, etc), and social rituals. Usually there was some point in placating the sacred by ritual or deed.
By this definition, religion is very widespread, existing in some form in almost every society and Hinduism is clearly religious. I'm pretty sure this kind of idea preceded his work by many decades.
That's the first point about his writings that I find hard to accept. The second objection is not scientific or academic, but political. I think his point of view promotes an anti-modern nativism of the sort that frequently leads to jingoistic nationalism.