There are no war between Hindus and Buddhists - if it happened maybe its a long time ago
However, this is what I found out
Revista de Estudos da Religiãosetembro / 2007 / pp. 157-164ISSN 1677-1222From which moment / period in time the Buddhist-Hindu encounter became manifest and what were the geographical and socio-cultural circumstances under which early encounters occurred?When emperor Ashoka (3rd century BCE) became a powerful patron of Buddhism, he prohibited the killing of animals. This was a severe blow against Brahmanism, because theritual sacrifice of animals was prescribed in the Vedas and formed a major part of the Brahmins’ livelihood. This made it very clear to the Brahmins that a state governed by Buddhists principles would hardly leave any space for them. Buddhism was now perceived not only as an intellectual rival but as a serious threat. And, under Ashoka – with his royal support – Buddhism rapidly spread within and outside the borders of his empire.
Hence it is not surprising that after Ashoka’s Maurya dynasty (2nd century BCE) we hear of fierce persecutions of Buddhism in India, inspired by Brahmanical circles.
Maybe I was misunderstood in this statement.
Which should have been Buddhist have an on going religious war on their own
and the Hindus have an on going religious war on their own too
And to clarify things, I did not use "each other" or "against each other"