My compatibility with Tamils (and a very, very good friend of mine is Tamil) would be on the basis of a shared language (English) respect for each other's beliefs (he is an agnostic/atheist Hindu and I am an agnostic Muslim), shared liberal/Western values ... etc.
It is the US/West that makes us compatible by giving us a common set of linguistic and cultural values to coalesce around, not some 'Indic culture' or 'Indic nationhood'.
When I say 'lack of compatibility', I am referring to a native Punjabi vs a native Tamil/Bengali - they have no shared language (excluding learning English), no shared values, culture and what not. You are ignoring those differences because you are viewing them from a 'global/Western commonality' perspective.