I would not be too sure of that for some North Indian Muslims especially that of U.P. but yeah most of the educated ones do get along very well especially South Indian ones.No idea about North Easterners.
SI also have problems especially our mujahidind type.But generally they dont give more importance to religion in their life.
On topic:Too bad our Guardians of entire Muslims dont even come in the picture even if they have world largest Muslim.population.