I think I would probably end up following--I say following and not necessarily worshiping--the Tribunal. I've always been very critical of the Dunmer and their native culture, but looking at the gods in the context of the world... here were gods who walked among their people, taught them what they knew, and, for a time, offered a real connection to the divine. I can't imagine being able to turn away from that.
If you're born a Dunmer, brought up in the Morrowind culture, taken part in interring your family in Necrom, the tombs, the Ghostfence... I can't see any reason why you WOULDN'T follow the Tribunal. Simply out of cultural respect and knowledge that the Devil is very real and ready to attack if anyone lets their guard down. Plus you are far less likely to be hung out on a limb as with the Daedra. Of course, we entered the Morrowind world when all that had started to decay, and with the Tribunal themselves withdrawing, doubt creeps into the Dunmer spirit...
Post-Nerevarine, I'm not sure there is much of a need for religion anymore, and you'd see a greater reversion to ancestor-veneration. When the Nerevarine abandons them and the Nords invade, well, I'd find it pretty difficult to find any kind of faith particularly when the Daedra are invading as well.