>Nowadays, lineage isn’t something that matters much.
they call it "caste" in indian subcontinent and unlike what the indian hindu ideology is around their caste system, everyone assumes that islamic lineage taking is same as hindu caste division which is not it.
> Hinduism started with "a great war". Buddhism started with a war.
This is an interesting take on Hinduism and Buddhism. I am assuming you are referring to Great Wars of Ramayana and Mahabharata. Everyone participating in those was were the followers of Sanatan Dharma which is known as Hinduism today. Both wars weren't fought of religious ground. Buddhism started with Siddhartha noticing dukkha (pain) of life and leaving home to find solution.