Your narrative is also rather misleading; Islam has been in India since just after Muhammad and many early Muslims were traders, not conquering armies. "Islamic colonization" is a meaningless phrase here, as most of the "conquest" was done by Central Asian tribes with non-religious motives. It's pretty easy to draw a line from the Mongols to the Mughals (after all, Mughal is a Persian-Arabic derivation of Mongol) and the Mongols certainly weren't on a religious crusade.
Otherwise, it is an immensely complex story and situation and one-line summary rebuttals aren't exactly helpful. I'm not an expert on Indian history, but to paint it as a straightforward narrative is unquestionably false.
[1]https://archive.org/details/HeroicHinduResistanceToMuslimInv...