Portugal was also a fascist state and there was quite a bit of a movement in Goa for Indian annexation. If we look at the other European exclaves, elections were uniformly won by Indian annexationists by the 1960s. Had Goa had elections, it would have probably won by Indian annexationists just as in Pondicherry, but of course it did not.
Also, all the fears that India would destroy Goa’s unique culture proved unfounded, because it was given its statehood with all the protections that implies. It was mainly those fears that put some Goans on edge about Indian rule.
India will have more Muslims than any other country in the world, but I strongly suspect religions relations would be better than OTL without the horrors of Partition. I suspect you’ll see a Hindu-Muslim party coalition in the same way a Sikh party is allied to the BJP IOTL. This party will probably advocate for separate laws for Hindus and Muslims (unlike the BJP) and general religious rights. On the other hand, you’ll have the secularist INC as OTL, which will not be as socialist with the influence of more right-wing Muslim politicians. You’ll also have other parties like the successors to the
Unionist Party, the party of the dispossessed elites much like the OTL Swatantra Party, but this India will likely be a two-coalition system as well.
I wonder what will happen to Balochistan and the NWFP. IOTL, Pakistan has had severe troubles in those regions since independence. I think India will be no different in that regard.