Kashmiri culture, language and ancestral religions has all to do with Indian culture, the name itself Sanskrit in origin. BTW the Punjabi-Sindhis share nothing in common with Pashtun-Baloch historically until they became the part of Pakistan on the basis of common religion, there was always a difference between people East of the Indus and west of the Indus.
The claim of Sanskrit of being Indian is wrong. Indo-Aryan languages were brought from the Aryans (Indo-Iranian) and spread over Iranian plateau and east Pakistan and later over North India.
Dravidian Languages are the real "Indian" Languages and race.
Punjabis and Sindhis do have similarities with Pashtun and Baloch.
There are Baloch-Sindhi tribes. South Punjabis are mixtures of Sindhis and Baloch.
North Punjabis are also mixtures of Pashtun and Punjabis and Kashmiris.
Pashtun and Baloch are Iranian, Kashmiris are Dardic, and Punjabis and Sindhis are Indo-Aryan, together they are Indo-Iranian.
And all of them are ancestors of the Indus Valley Civilisation (Sindh).
North Indians and Bengals are Indo-Aryanized Dravidians.
And South Indians and Sri Lankans speak even today Dravidian languages.
There are some fair skinned North Indians but those are not of pure Indian origins.
One part of Punjab was seperated from Pakistan and half of Kashmir is occupied in India.
These people are not Indians.