Interreligious conflict existed, but almost entirely on the economic, social, philisophical, and political levels. What I mean by this is that it seemed rare that violence was committed due to religion and even rarer that people would use "holy war" as a justification before the arrival of Islam. This doesn't mean that religion wasn't used as a justification for conquest, no, the idea of the "Universal Monarch" was in part a religious one used to describe the ideal ruler which many attempted to be. Actual physical conflict or persecution was minimal and the evidence we do have is minimal.

Actually, the pre-Islamic sources for Buddhist persecution are pretty suspect. The one that gets shared often is persecution of Buddhists under Puṣyamitra Śuṅɡa is also a matter of some debate. While some archeological evidence indicates deliberate destruction of stupas exist, others were rebuilt around the same time. This doesn't mean the story is true or not, and the fact that we find in in several sources indicates that it was in wide circulation, and it DOES seem that Puṣyamitra was a Brahminical reactionary conservative. In any case, whether he persecuted Buddhists or not his descendents clearly patronized them, restoring Saṅcī and building Stupas and Viharas.

Interestingly, from the same source as the above (well the better known version), we get a story of Aśoka massacrinɡ Jains and Ājīvikas for drawing a picture of the Buddha supplicating to Mahāvīra. This contrasts what we know about him as a ruler and frankly seems farfetched. It appears a later fabrication by Buddhist monks as part of a deliberate attempt to portray him as a sort of Buddhist fanatic (at the end he is told to be moderate and then is).

The Mahāvaṃsa of Sri Lanka states that the unification war was fought over Buddhism, but that actually wasn't the case. In actuality it seems both kingdoms were held a largely Buddhist aristocracy but also Brahminical followers too. The King of the north was a member of Brahminical orthodoxy, yes, but the war appeared not to have been the holy war it has been portrayed as.

As we can see deliberate violent conflict was rare, even though legends and stories play it up to be more than it was. In fact, there was often a deliberate patronage of all sects by Indian rulers, even non-Indian ones. Temples were commissioned for Buddhists and Jains by Hindu rulers, especially under the Guptas and the largely Buddhist Indo-Greeks, Kuṣans, Scythians, and Parthians built Hindu and Zoroastrian temples. Even as late as the Turkish invasions, the Palas and Calukyas were patrons of multiple sects.

We can trace this tolerance back to the times of the Samaṇas, all of whom seemed to have advocated patronage and tolerance, respect even, of all sects, even if they didn't always get along (The Ājīvikas seemed to get along poorly with literally everyone else). While little remains of the pre-Mauryan dynasties, what is there does indicate patronage of various sects by all rulers, and the Mauryans definitely took such advice to heart. Aśoka's patronage of all sects seems to have been a reality rather than just propaganda and his message of tolerance was carried forward by his successors.

While Aśoka's policy of Dhamma may not have been carried forward by post-classical rulers, Dhamma as ethics was not unique to him, and was an important part in rulership. To the kings of India, Dhamma was not only a moral or ethical obligation, but a deeply spiritual one. And sense part of Dhamma was universal tolerance and respect for wise men, it was in their interests to put forth tolerance and respect. There was a practical reason as well, India was a multi-religious, multi-ethnic state. All religions had power and persecuting one could lead to disastrous conflict even among the smaller sects.

As for those other types of conflict, the various sects often competed for patrons to support them and to build projects for them. This was often achieved through the promise of "merit", the idea that helping a sect would lead to a favorable rebirth. The Philosophical arguments were rather in depth and involved long treatises on why the other was wrong. We can find this even within religions as the various schools would often refute others beliefs. Social conflict often came in the form of Brahminical ideas working their way back into society and the monks pushing back, like in the caste system.

This should not be taken as a condemnation of Islam or in support of the persistent myth the Islam destroyed India. But, there is remarkably little evidence of interreligious conflict before the Turkish invasions and afterword, well the Turkish chronicles gleefully recount massacring monks and forcible conversions. This isn't to say that there was always conflict, even the notorious Delhi Sultanate loosened restrictions at times and participated in some good old religious tolerance, but tension between Hindus/Jains and Muslims has been a dominant theme since the middle ages with the former pointing to the destruction of temples and the forced conversions (and sometimes using the eradication of Buddhists as an example) and the later citing anti-Muslim riots dating back to British rule and the bias towards Hinduism built into Indian law.

Edit: A mild addendum. We do see other religions being economically or socially repressed by certain rulers. For instance, a ruler would stop patronizing or forbid patronization of a certain sect, essentially forcing them to move elsewhere by cutting off their financial resource, or shame the other sect publicly. While there was little out and out violence, this did occasionally force mass migrations of certain sects. Similarly, the denouncement would sometimes involve public denouements of the founder of a religion, which caused sects to leave in disgust.