I don't have a problem with that. I am a hindu, and I have gone to Masjids with my muslim friends...they do the same...and nobody makes a bruhaha about it here... not so sure about your area.
And does somebody expect Indian muslims to have a different agenda from Government of India? If yes, for what reason? Only because they are muslims are Pakistan is a muslim country? Forget it friends, that's not going to happen. Things are much different in India. There are no 'Indian Hindus', 'Indian muslims', 'India Jews' etc. If it were so, APJ Abdul Kalam would not build us missiles, would not be our president. Pathan brothers would not win us cricket matches. A R Rahman would not shower his divine music here. You may need to look at the world after removing your thick religious glasses which are blinding you.
I do admit that terrorists get some local muslim support, but thats all. When some entity claims to be purely religious, they invariable get at least some support anywhere in the world. Thats true about all countries, all religions.