Groups like the Chechens, the Ingush, Abkhaz, Circassians, Avars, etc are indigenous to the region (at least, they were all in place before the Ottomans arrived in the region). To my knowledge, most of these groups were never fully Christianized (the Abkhaz, who are split today between Christians and Muslims, are an obvious exception, though they're actually a South Caucasus group) and never developed the strong religious institutions of the Georgians and the Armemians. They slowly become Muslim between the 16th and 19th centuries (that is, relatively late). Russia only moves to the region in the late 18th and 19th century, and Byzantine influence obviously is absent from about the 15th century. This leaves a long period where Ottoman, Persian, and Crimean influences were the most important (Georgia and Armenia were important influences as well, but neither were independent kingdoms in this period). I know very little about the details of their conversion, but there's no reason to suspect that they didn't follow the pattern for many non-monotheistic groups on the frontiers of Muslim Empires. That is, there were two primary mechanisms to their conversion: Sufi Mystics went out, and they converted some, and then their tombs became important sites of local pilgrimage. Additionally, the state's judges (qadi), who administered a lot in the periphery, were another important influence. As the local groups got worked more into the state-system, Islam was part of then"package" of civilization as much as literacy, agriculture, etc. I am not sure how some groups (like the Ossetians) ended up majority Christian. There's also a long pattern of joining the religion that opposes a rival group, so if these groups so their main competitors as Georgians and Armenians and later Russians (and I'm not sure they did, but if), then it makes sense that they would turn to Islam.