It actually has a genetic basis. According to David Reich in his outstanding book Who we are and how we got here, the varna/jati castes and sub-castes have been able to maintain a level of endogamy stricter than Ashkenazi Jews for millennia and there is 2-3x more genetic distance between two different jati groups coexisting in the same village than between North and South Europeans.

So basically you had a group of invaders who came to India, proclaimed themselves both racially and morally superior, and enforced a rigid system of miscegeneation laws to prevent themselves from being diluted. Makes the wildest dreams of white supremacists tame in comparison.

Of course, none of that justifies the discrimination. I don't know how to fix it either, India tried but hasn't succeeded. B. R. Ambedkar, the author of India's Constitution came to the conclusion that Hinduism is unreformable and that former untouchables like himself should convert to Buddhism, but that hasn't happened on a large scale. Subhas Chandra Bose proposed to abolish the caste system through socialism and inter-caste marriages, but he was an authoritarian bordering on Fascist.