One of the Major causes for the Stormcloaks rebelling against the empire would be that they banned the worship of Talos.
The Empire they are fighting against was Talos' Empire once. Talos would not have wanted his Empire weakened even further because of the Stormcloaks. They are going against Talos?
1) Talos said in Morrowind that his empire was gonna fall. Didn't seem to bother him much. 2) This is Mede's empire. The Septim line died with Martin. 3) As a god, Talos likely doesn't give a crap about the empire anymore. 4) As a god, Talos would care about his worshipers, for they are what shapes him.
"The Emperor is getting old. Don't know how much longer he'll hang on. So is the whole Empire, for that matter. Getting old, that is. The Emperor and the legions have held the Empire together for hundreds of years. It's been a good thing, by and large. But maybe it's time for a change. Time for something young and new. What? No idea. Because I'm old. Old dog doesn't get new ideas. But maybe young folks like you should try some new ideas. I don't know. Could be messy. But change is never pretty." - Wulf, avatar of Talos
I don't think Talos cares much about the Empire anymore, not when they are a part of weakening him.