The British and Mughals were fine with the caste system. Caste is a pan Indian social phenomenon found even amongst Muslims and Christians (and Jews) of the subcontinent, as well as the dharmic religions. I agree that there's a bizarre desire to only acknolwedge the Islamic empires, but I'm not sure it's about caste.

Britain in particular was completely into the caste system and made huge lists of which caste ought to fill which roles in its government.

All of this is problematic of course. However while its fairly easy to criticize England in the Indian context, it is bizarrely difficult to criticize the Mughals because some people are offended should anyone in their religion ever be criticized