The battle of Kurukṣetra was not about promoting one religion over another. Ultimately it was about establishing righteousness. The Pāṇḍavas were the legal heirs of the kingdom, and their cousins, the Kauravas, had usurped the throne. The Pāṇḍavas represented dharma (righteousness), whereas the Kauravas embodied adharma (impiety). You can read more about this in Bhagavad-gītā Chapter 1 – Sainya-Darśana (Observing the Armies on the Battlefield) – Verse 11 and the Anuvṛtti