Islamic invasion in India, is not a new phenomena, however in your question you are asking about paki, before 1947 it was a part of the British India, there was no pakistan.
When did pakistan invade India? Pakistan itself was invaded by Harappan, Indo-Aryan, Persian, Grecian, Saka, Parthian, Kushan, White Hun, Afghan, Arab, Turkics, and Mughals.
Accepting your question in the broader sense of Islamic invasion, I can only quote from history, that the moghul rulers did respect some respect some secs of hinduism. THE MUSLIM AGENDA WAS ONLY INVADE INDIA AND NOT TO MAKE HINDU'S AS MUSLIMS.
In my opinion if one had to make a cultural damage to hinduism one has to understand hindusim. I completely agree with Cheif Justice of India Gajendragadkar. "In 1995, Chief Justice P. B. Gajendragadkar was quoted in an Indian Supreme Court ruling
"When we think of the Hindu religion, we find it difficult, if not impossible, to define Hindu religion or even adequately describe it. Unlike other religions in the world, the Hindu religion does not claim any one prophet; it does not worship any one god; it does not subscribe to any one dogma; it does not believe in any one philosophic concept; it does not follow any one set of religious rites or performances; in fact, it does not appear to satisfy the narrow traditional features of any religion of creed. It may broadly be described as a way of life and nothing more."
Even today I have noticed new vinayaka's and mariamman's and other gods and godesses apprearing, which was not heard before, new thoughts, superstitions, dogma is developed every day.
My conclusion is no one can have a clear agenda to defeat hinduism, because hindu's worship the Kabha and Jesus picture in their homes. Hinduism accepts Jesus and Mohammed as one of the avatars, and they are waiting for the Kalki. The BJP/RSS/Shiv Sena/Bajrang Dal is trying to fish in troubled waters without knowing the heart of hindu.