SORTED (partially) after a 45min call with Apple Support. Yes, I'm from India and yes, I have exactly the same problem of "Music and Podcast" being greyed out. Two step process that worked for me:
1. Turn OFF family sharing
2. Go to iTunes store and change store from India to US.
Everything worked.
However, this is only a temporary measure because I can't use my Indian credit card in the US iTunes store (it asks for a US address and I don't have one). And I can't use the Indian iTunes store because all explicit content has been blocked.
I hope this gets resolved.
Hope this works for everyone else too.