Do you (and Dalyn) think that the fact that the rest of the world isn't "on board" is significant. Russia has the Caucasus. China has the Uighurs. Still, we're working at cross purposes. Which is more likely: that the threat you've described is indeed a threat to all non-Muslim nations, or that the threat is being manipulated by all sides to achieve political and strategic goals.
Think back to the GWB War on Terror days. Putin was glad to embrace Bush and decry the menace of terrorism because it gave him latitude to operate in the Caucasus without restraint. Turkey refused to let us use their airspace for OIF in part because of our relationship with the Kurds in northern Iraq. I had two Turkish friends that I talked to a good bit in those days and they were fond of reminding me that, while Bush was declaring a global War on Terror, their country was the frequent victim of terrorist bombings carried out by Kurdish separatists. Those Kurds were friends of our friends, or at least enemies of our enemies, so the violence against the Turks somehow didn't rate. The rabid anti-Bush sentiment in Turkey was mostly just manipulation and misdirection by Turkish politicians, but it was at least grounded in legitimate opposition to that hypocrisy.
I'm sympathetic to your point of view, but I see a tendency towards oversimplification.