Nice to see you never read my post even though you quoted it. The Chechens were nationalist separatists first. They've only recently (within the last ten years) become dominated by the more Islamic Radicals.
They wanted to leave Russia like all the other republics that left the USSR, and the Russian gov't didn't let them. It was not religious in nature for the first 15 years after the fall of the USSR. Of course, they've been rebelling pretty much since 1905.