Skyrim had been under Imperial rule for a good part of it's history. (Reman era, Septim era, and the Mede Era for now.) So it is understandable that either the Nords slowly accepted the Imperial Divines, or the Imperial Cult slowly converted the population into their own religion instead of their filthy barbaric ways. And one would expect this process to be going on since Tiber Septim took the throne. (Or maybe even Reman himself.) However their's a problem.

IIRC, in Oblivion, some of the characters in Bruma mentioned some tension between the followers of the Divines and the followers of the traditional Nordic religion. So by the end of the Third Era, much of Bruma's population seemed to follow the traditonal Nordic religion. So that would mean that it's pretty popular up north in Skyrim by that time.

Now fast forword two hundred years into the future. Almost all of Skyrim follows the Imperial religion. Even the "traditional" Stormcloaks believe in the 8 i mean 9 divines. (One of the main reasons why they're even fighting a war is over one of those gods.) So that means the change was more recent and sudden. Question is, how and why?

The only hint I could think of is that there was a sourve (I forgot where) that mentioned that the Empire was starting to become unpopular even before the WGC and the Civil War. So is it possible that one of the Mede emperors, for some reason, pushed the Nords into his beliefs, thus causing the eventual dissent among some Nords to the Empire?

I see it more like this: if we are going to weasel Bethesda out of what was likely just an oversight, it makes sense to imagine that in the post-Septim era, a sort of Imperial fetishism became popular. Just as after the fall of the Western Roman Empire, the German lands who had never been a part of this Empire took it upon themselves to be the bastions of the Holy Roman Empire, a particular brand of 'Talos as Nordic Conqueror' version of Imperial revisionism became incredibly fashionable in Skyrim. It is not hard to imagine that while Cyrodiil might have been war-torn and even rife with Daedra worship, the Imperial Cult in Skyrim took over the old Imperial religion's new centre. Fast forward 200 years, and we have the strange status quo we find in TES:IV Skyrim.