I think it is ridiculuous to ask the question of whether India did the right thing in 1971. India has always stood for peace and democracy. We could not have tolerated inhumane atrocities by the Pak military on innocent people. Moreover, the 1971 war was an ideological victory for Indians over the principle of two nation theory.
Nations cannot be built on religion alone. If religion would have been the sole uniting factor there would not have been so many arab nations, all muslim and all speaking the same language.