The notion of moderate Islamic states there is fascinating - I was aware that fundamentalist Islam in Chechnya was apparently a response to Russian brutality there - not intrinsically Chechen.
When, in the early 18th century (1721?), Petr Alexeevitch conducted his last military campaign on the shores of the Caspian Sea, he sent a column to impress the Chechens and the Ingush with the military might of his new empire. They were not impressed. They slaughtered about 3,000 Russians. They had been primitive, blood-thirsty tribesmen when the Seljuk Turks had
impressed them, in the tenth century. They became Muslim more or less in emulation of their erstwhile masters. When Tamara became the Queen of Georgia, they had been cozened into joining the forces of Georgian nobility who opposed her. She repressed those tribesmen brutally. They saw it more as a case of a demonstration of the inherent evil of Orthodox christians, than as a religious war. After the Mongols and their client army, the Tatars, swept through the region, and ended the Georgian kingdom, the Caucusus tribesmen remained aloof, and later allied themselves to the Tatars on more or less the same basis as they had with the Turks. When Peter the Great's troops showed up, it was, to them, just another case of Orthodoxy attempting to crush them--although, again, with the caveat that they did not necessarily see it as a religious war.
Peter's mad daughter, Elizabeth, sybarite and all around ill-tempered autocrat, married her son to Sophie of Anhalt-Dessau, partly at the instigation of Frederick the Great. Sophie eventually deep-sixed her husband, and using Ekaterin, the Orthodox name she had taken, she became the Empress Catherine II, Catherine the Great. As an old, old woman, she took her grandson, Nicholas, into her household to raise. She imbued him with her prejudice against the Russian nobility, although he did not understand that she despised them because she was German and they were not. He only imbibed the attitude of the autocrat. Raised to be profoundly orthodox, after the assassination of his father (a Russian diplomat once commented to the English minister at St. Petersburg: "Assassinations, that is our constitution."), he was chosen by the higest aristocratic families, as his elder brother was considered feeble-minded. Dissentient nobles attempted a coup using his brother, and failed, and deeply reinforced Nicholas' suspicion of them, and determination to rule in a completely autocratic manner. He published a slogan: "On Mother Russian, one Church, one Tsar." He meant it, too. As long as one was willing to surrender their native language for Russian, practice the Orthodox religion and swear (upon pain of instant death for betrayal) eternal fealty to the Tsar, they could be his buddy.
At the time of the Russo-Turkish war which became known as the Crimean war, ethnic groups in remote areas tried rebellion, but most caved in pretty quickly. The Chechens and Ingush, however, proceeded in the manner to which they had become accustomed, and slaughtered all the Orthodox people who could not escape. In 1855, at the height of the debacle at Sebastapol, Nicholas dispatched a large army to the Caucasus. For the next 23 years, the Russians hunted down all the tribesmen who would not accept Orthodox baptism (i.e., most of them), and slaughtered anyone in their path. It was a bloody campaign in which far more Russians lost their lives than in the late war.
There were petty uprisings thereafter, quickly crushed. In the First World War, the Chechens were brigaded together, and a Chechen division was used by Kolchak in his attempt to put the Petrograd revolutionaries out of business. Thereafter, the Chechens allied themselves with the White Russians, and enjoyed a tenuous autonomy for a generation. Then they were subjugated by the Red Army. In the Second World War, they allied themselves to the Germans, in yet another attempt to get out from under the Russian thumb, and to avenge themselves. In 1944, Stalin, as Nicholas had done before him, took significant military forces and diverted them from the main campaign, sending them into the mountains to crush the Chechens and Ingush. The Chechens who survived were rounded up and deported to central Asia, more than a thousand miles distant. They were not repatriated until a generation later, long after Stalin's death.
The bloodshed between Chechen and Russian has religion as a veneer, but the motivation is a deep tribal hatred and blood lust on both sides. An independent and viable Chechen state would be moderate Islam, because Islam has laid lightly on their culture, as was the case with the Balkan Muslims of Bosnia-Herzegovina. But the Russians will likely never allow it, and the slaughter will likely never end.