There is a non-zero number of Kashmiri Hindus who are partial to having independence. Their rationale is that "Kashmiri Hinduism is different from mainland Hinduism". The issue with that thought is that there is no "mainland Hinduism". You will find different variations of Hinduism all across India. Tamils will have different traditions than Bengalis and Marathis and vice versa. For example, groups of Marathis and Kannadigas worship Sri Sai Baba while in UP and Bihar, they follow the teachings of Swami Karpatri Maharaj and Bengalis follow Sri Ramakrishna Paramahamsa. And even within ethno-linguistic groups there will be variations due to different Sampradayas. There are also the Tulu and Konkani people who have merged their folk deities called Daivas (not the same as Devas) with their Vedic worship of Parshurama.
Knowing all this means that the thought of "our Hinduism is different from yours" applies to every single Hindu in the world. So this is a very flimsy argument to make for independence or even autonomy because why should Kashmir have a distinct status from every other state which has their own version of Hinduism? By that logic, should every village become their own country because they have a different Kula Devata or because they dress the same Kula Devata in a different way?