The thing is that most Nords have no problem with the Empire. They have a problem with the Thalmor. Although battles are fought and people are being killed, the Stormcloaks are relatively merciful. For example, I can't remember a single Jarl being executed by them at the end of the questline. If it was the Thalmor, we'd never hear from those Jarls again.
Visit Riften: Imperial sympathizers are arrested and one of them asks you to stay quiet about his dislike for Ulfric least the SC's kill him. The Imperials on other hand let SC sympathizers roam freely as long as they don't outright join them.
If you tell Galmar you want to think through about joining the SC, he will threaten you while if you tell the same to Tullius, he will respect your opinion.
The method of occupation is similar, but the enforcement of laws isn't. Windhelm, the Stormcloak's capital, has Dunmer, Altmer, and Argonians. They don't lead the best lives, but they manage, and sometimes do well for themselves. The Thalmor, on the other hand, regularly purge areas of ANY foreign influence, whether that be genetic or ideological. And it usually involves burning corpses.
Skyrim started to become just that, and the Empire was spread too thin to appropriately defend them. As a result, the Empire was forced to allow the Thalmor to begin purging inhabitants under the pretense of the WGC. Of course, the Thalmor are somewhat restricted by this, but the rebellion is to stop them from gaining any more power.
The Thalmor capture worshipers yes, but the rebellion doesn't necessarily mean it would be good on the long roads. In case Cyrodiil falls and Skyrim fails to defend itself due to its military power being wasted in the Civil War, then... well, I don't think I need to say what Thalmor will do without any restrictions...
The current state is temporary. The Empire prepares for another war and reading Thalmor Dossiers you can see that they already accepted the fact that the peace won't last. And once it ends, the Talos Ban will be lifted and the Thalmor agents will get massacred by vengeful Imperials.
So it goes down to...
1) remove Thalmor influences now but the risk of Skyrim falling to Dominion increases (SC side)
2) tolerate Thalmor agents for now but chance of Dominion's defeat increases (IL side)
Furthermore, this rebellion absolves the Empire of any obligation to enforce the Concordant in Skyrim, allowing both parties to amass armies in preparation with war against the Thalmor. My personal hope with siding with the Stormcloaks is that the Empire and Skyrim would work together in the upcoming war.
Hate can make one blind to reason. I find it highly unlikely that the two sides will shake hands and more likely that Nords will hope Cyrodiil kills enough elves that they can defend their own land from the Dominion.
However, what I think Nords don't take into consideration are the Ayleid ruins in Cyrodiil and the Dawn Magics the ancient Ayleids had. If Thalmor get their hands on them and Ayleid artifactsit is likely they get enough power-ups that Thalmor gets our stronger after Cyrodiil's fall.