Since people ask me this I have to post this now and then. We have genetic data. So in short order
1) Kashmiris are like other people in the Northwest of India. They are not enriched in steppe ancestry, at least compared to many Punjabis or Brahmins from the Gangetic plain
2) There is no genetic difference I can see between Pandits and Kashmiri Muslims, indicating to me that one distinctive aspect of the Vale of Kashmir in comparison to the rest of the Indian subcontinent is that it does not exhibit the jati-varna structure common across the subcontinent
3) Some researchers and genetic genealogists have found some Tibetan admixture at low levels among Kashmiri Muslims and Pandits
4) It is probably correct that elite Muslims have low levels of Central Asian and Iranian ancestry, though that’s harder to detect than Tibetan background