I don't have specific sources referring to Chander Bhan in particular, but for the Mughals I can tell you that effective rule was a higher priority than spreading Islam or keeping their court "pure". The Mughals were very smart rulers and wanted the smartest people to help them govern.

They understood that local Indians who were Hindu and could relate to the population at large would be great liaisons for effective administration. People like Birbal in Akbar's court were highly respected and brought a lot of insight to the table.

Even during the period of Mughal rule, local Hindu kings were still allowed to have power. They just reported to the high-level Mughal administration. (Talking about North India specifically; Vijayanagara and other South Indian kingdoms were a totally different world.)

As far as hiring people within the Mughal court goes, they would prefer to have people who were familiar with local customs and laws. Also, having to "import" people for leadership roles from other Muslim empires in Central Asia would be expensive and annoying. Using local talent and forging loyalty to the Mughal empire was more efficient.

(Fun fact -- Akbar was actually illiterate [possibly dyslexic] and had to have everything read to him!)

See: "India before Europe" by Asher and Talbot. Amazon link.