So "ascetic warriors" were definitely a thing in medieval India (and still have a foothold in Indian militia organizations today), but the description you are asking about is very misleading.

To start, a point on terminology. Indian ascetics went by a number of names, including sanyasis, gosains, bairagis, faqirs and nagas. It is important to note that "Hindu" ascetics often used an Islamic term (faqir) and Muslim ascetics often used "Hindu" terms. In fact there was no clear distinction within many "renouncer" militias between "Hinduism" and "Islam," especially since these terms failed to penetrate deeply into Indian society for a considerable period of time. The key point here is that Muslim faqirs and Hindu sanyasis frequently collaborated or formed coherent organizations with little apparent dissonance, well into the British period in fact.

Communalism is a whole debate unto itself, but there is substantial disagreement on whether there was even such a thing as "communal" conflicts prior to the late 19th century. For a decent overview of this debate, see Bayly, Christopher A. "The Pre-history of ‘; Communalism’? Religious Conflict in India, 1700–1860." Modern Asian Studies 19, no. 2 (1985): 177-203.

In short, there were some conflicts along communal lines, but there was a more widespread and deeply ingrained "synthesis" or "syncretism" between Islam and Hinduism in India. There are some exceptions that people like to bring up (say, the Mughal emperor Aurangzeb, a pariah among Hindu scholars), but even those are contested. Whenever there was Hindu military agitation against Muslim conquerors, it was less understood as a fight between (irreconcilable) faiths, and moreso as a political resistance to unwanted invaders. Hindu polities frequently allied with Muslim groups and states to protect themselves, and Muslim armies often allied with Hindus. Ascetic militias emerged in this very milieu.

Martial asceticism has some putative linkages in South Asian legend and myth, but the consensus is that "warrior ascetics" as we know them largely emerged during the Mughal period, not out of conflicts between Hindus and Muslims, but rather as a network of syncretic mercenary militias that facilitated the Mughal state's consolidation of its empire. Over the course of the following several centuries, their power and notoriety ascended before reaching a peak in the 18th century.

We must also emphasize that the "martial ascetic" is notable primarily a symbol of Indian patriotism in opposition to British rule. As such they became fixtures of popular culture that are intended to represent a long tradition of austere Indian masculinity and martial ability. This is also the reason for its continuing presence in the popular imagination -- it cuts against the common association of asceticism with vegetarianism, non-violence, perhaps even femininity or weakness. This is an understanding of "asceticism" that is far different from what many are accustomed to in the West. In many ways, political leaders today present themselves as martial ascetic figures (in both India and Pakistan), but that is a topic for another time perhaps.

Ultimately, the answer to your question is basically no. Overall, military orders of Hindu ascetics cannot be primarily (or even secondarily) attributed to communal conflict.

The best source on these topics would be various works of Vijay Pinch (also published under the name William Pinch):

William R. Pinch, “The Slave Guru: Masters, Commanders, and Disciples in Early Modern South Asia,” in The Guru in South Asia, ed. Jacob Copeman and Aya Ikegame (Routledge, 2012).

Pinch, William R. Warrior Ascetics and Indian Empires. Cambridge University Press, 2006.

Pinch, Vijay. "Gosain Tawaif: Slaves, Sex, and Ascetics in Rasdhan, ca. 1800–1857." Modern Asian Studies 38, no. 3 (2004): 559-597.

These would all be a good place to start.