They might call it caste in English, but in Urdu they call it Baradari/Zaat. My family is Urdu Speaking, as in they came from UP to Pakistan during partition, and they had called it Zaat. However at least the ones who came to Karachi have intermarried over the generations, and no one cares anymore about that anymore.
Its more of a socio economic issue than a caste one facing Muslims. Muslims will socialize with people of the same socio economic standing. Here is an article on some Mughal descendants living in poverty.
https://www.dailymail.co.uk/news/ar...um-washes-street-struggles-feed-children.html
Do you think they are enjoying any privilege? Do you think they will get invited to high tea with some upper middle class Muslim family? If they weren't able to prove descent from the Mughal family, most people would call them liars because of there skin color, and say they are deluded in thinking they are descent from the Mughals.
Second like i mentioned a lot of those people with the "foreign" surnames would have just changed there surnames. Its impossible to prove in 2020 who is descendant from the people who came from other countries and who were the locals who converted and changed there surnames. You cant go by skin color, or socio economic status, or even surname.
Anyway there is a huge difference in the Hindu Caste System and the Muslim Baradari/Zaat. Hindu caste system decides on the occupation one does in perpetuity. There is no required occupations based on your zaat. Not to mention restrictions on going to the Mandir, while there is no restriction on going to mosques based on zaat.