During medieval times there was seldom a clear-cut difference between Hindu kingdoms and Muslim kingdoms that were founded in the subcontinent (like the Bahmanis). In fact the name of the Bahmani Sultanate comes from a brahmin named Gangu Bahmani, who was the patron of Alauddin Hasan (the founder of the Sultanate). Alauddin Hasan adopted the name Alauddin Bahman Shah in honor of his patron, and Bahmani subsequently became the dynastic name.
Both Hindu and Muslim polities had in their courts members of both religions, and their methods of governance were more or less similar. The real polarization comes when you compare established kingdoms of the Subcontinent (whether Hindu or Muslim) with the semi-nomadic warrior hordes of Central Asia. For example, the Delhi Sultanate and the Timurid Empire were both "Muslim" polities, but one was an established, agrarian kingdom typical of the subcontinent while the other was not. Despite their shared religion the Delhi Sultanate suffered extensively at the hands of the Timurids, due to the great differences between them from both a political and cultural standpoint.