The Sons and Daughters of Skyrim want freedom from a foreign Empire that seemingly doesn't care about them. An Empire that, in their eyes, bans their God and then starts prancing around with the Thalmor after a whole damn war with them, without even asking one Jarl about it. This! From leadership in another country! It might as well have come from another continent to them!
They may not have the most logical conclusion, but they are humans, which are creatures of emotion, not logic.
Independence from the Empire sounds good to them, so why not fight for it? The Empire resisting makes them even more assured in their cause.
To them, it would be better to be independent and openly oppose the Thalmor rather than the Empire that, in their eyes, lets the elves hop about Skyrim anyway, seizing Talos worshippers and murdering them in the night.
And honestly, could you blame them?
You seem to focus only on the long term goal of Skyrim surviving. Not the people of Skyrim that live within it. The very people who form Skyrim.
Many in Skyrim are neutral on choosing sides, but many worshipped Talos, so they are generally happy when Skyrim is liberated by the Stormcloaks. Many are indifferent, so luckily it wouldn't impede them much who's running things.
(I'm talking mainly about Stormcloaks and those who agree with them, the battered imperial supporters should probably just leave Skyrim if the Imperial Legion retreats.)
Why now? Why not twenty six years ago or even ten years ago?
The Thalmor stirred things up, but why do it now? What has changed, the entire Imperial Army on their doorstep for one. The Empire had a six year head start in preparing for the second round of fighting, the rebellion effectively turns the Empire's attention away from the Thalmor and onto petty internal disputes.
Why should the Stormcloaks get a pass because they're not thinking logically, I can focus on the people living in Skyrim. They had little problems, Thalmor were very limited, things were fine.
Come Ulfric and his Son's of Skyrim, well what the common citizens tell us is that things got a lot worse. Speak with many NPC's and listen to their conversations.
1) People are starving
2) Roads are too dangerous to travel for villagers
3) Many merchants have fled Skyrim
4) Bandits are raiding farms
5) Prices are extremely high that even Jarls can barely afford to keep their city stockpiles up
I should support the Stormcloaks to make Talos worship legal? At the cost of isolation, possible starvation, slavery and racial problems to rise.
When does it become too high a cost? How many should suffer so Ulfric can selfishly take the throne, yes even Stormcloak supporters are saying he only wants the throne.
Tullius was able to best the Thalmor at their own game in capturing Ulfric. That gives me hope for the Empire, but not the Stormcloaks since they don't even understand the Thalmor threat. They're just enjoying the illusion of pushing the Thalmor out of Skyrim.
I'd take the painful truth over a pretty illusion any day. Skyrim has every right to become independent, but not with the Stormcloaks. Or at least until we kick the plops out of the 'Old Mary' Dominion as the Legion calls them.