No they are not causing fitna or fisad based on the fact that the legitimate government you are talking about was imposed on them by force.
At the time, the legitimate government, "The Raja Hari Singh", acceded to India.
Remember that islam does not prescribe democracy as the only legitimate government.
Any government that permits the free practice of the deen and does not cause harm to the local population is a legitimate government.
The indian govt. fully qualifies in all of these criteria.
They weren't given their right to decide what they want.
No one says they had this right, do you think that every village and town with more muslims than hindus can choose to be independent?
Islam does not give you this right.
You have the right and duty to be part of the government
Kashmiris have full rights to participate in the Indian govt, legally.
Violence against the indian state in this case is fitna and fasad, it is unislamic, and must be condemned in the strongest of terms by believers on both sides of the border.
They were forced to remain in Indian dominion with tyranny and brutality. So they are struggling against tyranny which is toally acceptable according to Islam and which is totally Islamic.
There is no tyranny and brutality from the government.
There is alot of prejudice (and unfortunately violence) from hindus and sikhs in the name of religion.
However, the problems of the kashmiris have been caused in large part by their own unislamic behaviour and the behaviour of some pakistani brothers.
I will compromise on any matter, but not matters of the deen.
I may not like what I see in Kashmir from the indian armed forces.
But I also know that the kashmiri muslims have abandoned islam and are following a nationalist agenda being encouraged by the pakistanis.
What can you expect as a nation when you ignore the warnings of Allah(swt) in the Quran?