It was a question that sprung into my head while I was reading about the outline of the first Islamic incursions into the Indian subcontinent? I know there were three main religious groups active in India during this time; Buddhism, Jainism, and the Vedic Hinduism (as pointed out by /u/Valmyr5) (I know Hinduism is too monolithic, I suspect that's the case for the other two as well, and the small populations of Christians, and Jews are barely significant for me to consider for this question), but did they cause any sort of religiously inspired warfare?
I am not an expert, and my knowledge comes from literary history; it is also limited to Western India, but I will try to answer this.
As far as traditional Hinduism goes, there was little religious conflict. People from all over the Indian subcontinent often revered the same holy sites and made pilgrimages there. Taking Somnath Patan temple for example, pilgrims from modern day Gujarat (then Kucch, Lat, and Patan), Sindh, Malwa, Chedi, and the South traveled months to visit the temple. They were often looted by bandits or local smaller kingdoms, but as far as religious warfare goes, there was little to none simply because everyone adhered to the same faith.
There was some friction between Jains and Hindus. I say some because in those days Jainism had diverged little from Hinduism and it was not uncommon for people to practice both faiths. However, for the most orthodox of Jains or Hindus, this was not a trivial matter. We know that Chanakya (mahaamatya [prime minister] and teacher of Chandragupta, and the brains behind the Maurya dynesty) was slightly disappointed when Chandragupta adapted Jainism later in his life.
Much later, in Western India, we know of some friction, if not actual warfare, between Jains and the Solanki (Chalukya) dynesty- especially in times of Karnadeva I and Siddharaj Jaysinh (1064-1142).
This was after Mahmud Ghazni's two campaigns throughout India, so technically, at this point, Islam is introduced, but since Mughals have not arrived yet, I'm going to oversee that.
Jain merchants were gaining a lot of power through wealth and started to enter politics. Jain cities, like Chandravati, were starting to gain influence in the Solanki courtroom. Wife of Karnadeva I, Minaldevi, also a Jain. As a result, there was obvious resistance from the orthodox Hindus on basis of religion, as well as political resistance, simply because of a newly emerged political power.
Do keep in mind that at this point, many still considered these two to be the same religion in practice, so when we talk of friction, it is mostly limited to an orthodox minority and politics.
Lastly, there are some literary legends of a minority of Jain monks who sought to unite Gujarat, and later, the rest of India, under a zealous Jain faith to counter the growing Islamic threat from the West. They believed that Muslim invaders like Mahmud Ghazni can only be countered by an equally zealous people, united under one faith; this put them at odds with the more tolerant and libertarian majority. But I can't vouch for its historical legitimacy, this is just an interesting point that I have come across in various literature.
You're probably trying to be inclusive when you say "Vedic faiths" but you're misrepresenting Hinduism by omitting the shramanic content.
Hinduism is a syncretic religion formed by the blending of Vedic and Shramanic traditions. Many of Hinduisms key features are Shramanic, not Vedic. In fact, some of the oldest branches of HInduism, such as Shaivism, are Shramanic. Shiva was not a Vedic deity, but he CAN be found in India before the Vedic people arrived. Indus Valley seals dating to almost 2,000 years before the Vedic people show him in his Rudra/Pashupati incarnations.
"Hinduism" is the better term than "Vedic Religions" in my opinion, because it includes the huge non-Vedic component that existed in India prior to the Vedic people. It didn't get obliterated, it's very much alive in India today and has been for many millennia.