Kamala Khan's family are Pakistani muslim immigrants living in New Jersey. When they talk to each other, their language is identified as Hindi. Big part of their characters background is their experience during the Partition.
How likely would any of this be in the real world? Were Hindu-speaking Muslims common in India and how would they end up in Pakistan during the Partition? Would they identify as Pakistani? Would it make more sense for these characters to speak Urdu?
There are many aspects to this question but some basic facts that might help give you the lay of the land first.
The concept of "India" has been fluid over the millennia that region has been inhabited. From BC times different rulers and kingdoms have existed that have reigned over different overlapping parts of the subcontinent (and sometimes beyond).
Present day India, therefore, did not exist until sometime during the British empire. At the time, it would have covered regions stretching from Afghanistan in the west to Bangladesh in the east (north-south it is bound more rigidly by geographical features: the Himalayas and the Indian Ocean). At this time, it was a region defined less by nationality but more by regional identity and princely states that reigned over the regions.
India and Pakistan only became two separate nations on August 15th, 1947.
The Partition of India in 1947, one of the most significant events in thousands of years of Indian history (and also the biggest mass migration in the history of the world with over 10 million people displaced) was the moment in time that divided that region into India and Pakistan. Millions of Muslims from regions east of the border moved to Pakistan and millions of Hindus moved east to India creating a Muslim majority state in Pakistan (the rest of India was already Hindu majority).
Of the regions that were most impacted (and the area that fell over the border on both sides) the mass of land known as Punjab (the land of 5 rivers) was divided between the two countries.
Now to come to your question. Linguistically, the primary languages spoken in this region are Hindi (different from Hindu, which is a religious identity), Urdu and Punjabi (I'm only focused here on these but note that there are many different languages spoken in the rest of the country). Urdu, while written in the Persian script, is very closely related to Hindi and is spoken like Hindi. In fact, everyday spoken languages in these parts Hindi and Urdu are so similar that it is difficult to differentiate between the two (one perceptible difference is Urdu has many more Persian words than Hindi - which makes historical sense because Urdu came into being during the period of significant Islamic conquests of that region: 12th - 16th century AD and beyond). When Pakistan was created, Urdu was adapted as its national language (among others, for political reasons). And thus there was this somewhat manufactured difference created between the languages based on national borders.
So yes, it would make sense that Urdu-speaking Pakistanis would speak a language that is similar to/indistinguishable from Hindi (because they do even today), and that it would possibly get classified as Hindi by folks who might not know the minute differences e.g. Hollywood.