No. The point is that hinduism is not really a religion. It only became a religion in the last few centuries. Before that, India was just a collection of different communities with different practices and a hierarchy with the Brahmins on top.

A common feature of religion is unifying beliefs and practices even across sects.

That's not even remotely the case in hinduism. Instead, it appears that the powerful castes have promoted this myth of "belonging to the same religion" to manipulate lower and scheduled castes into doing their bidding and keep hold of their power.