Islam, Christianity came to Bharat much later in history, Buddhism, Jainism come out India also but later. Most of the other religions that have invaded this land called Bharata or as it is now called "India", have come later after the Vedas, the Vedic culture. They have come for purposes of conversion.
Indian's as they are now called are very tolerant, they allow others to practice their own religion, create their own version of what today is know as Hinduism or Sanatan Dharma, perhaps they never thought anybody would squeeze them out, or from years of being a conquered land, and people they developed an inferiority complex, just wanting to be accepted by everybody.
To say India is not Hindu or Veda is to dismiss history. Did the indigenous people of India originate in Saudia Arabia, or Isreal, or Europe, no all the stories, ancient art, ancient sastra all point to the land mass now called India.