This question is rather deep, and there's not a lot of information given to you on the geo-political status, but I'll try to explain as best I can.
At the end of the war with the Thalmor, the empire was actually in a winning position, the emperor just ceded the conflict and gave into their demands for whatever reason. Afterwards, the Thalmor remain in a severely weakened state, help up only by their status as victors. If the empire were to go to war with them during the game's events, it would result in the empire's victory due to not only to the fact that all the territories under their control resent the Thalmor rule, but because they're still recovering from the last war. Hence the game's events, you find evidence indicating that they want Skyrim to secede from the empire, as that would weaken the empire greatly and put them on more even terms.
When looking at the two leaders of the rebellion specifically, Uflric Stormcloak and General Tallius, they both essentially want the same thing. Freedom from the Thalmor. It's implied by Tullius that he intends to lead a military coup against the Emperor in the event he bows to any more Thalmor demands, but that the time is not right, the empire has its own wounds to lick. Obviously that would be a good thing in the long run against the Thalmor.
Ulfric wants to take the more direct route, being a hotblooded nord, what's not evident is that Skyrim seceding would not be a completely bad thing for the empire, as they still have deep connections going back to Tiber Septim that would be unconditionally honored, even if they were a separate state. Ulfric is tired of the Thalmor dictating empire affairs, seceding from the Empire would release the empire from enforcing the terms of the treaty to them, but also put them at risk of being conquered by the Thalmor in a conflict the Empire may not be ready to fight, especially considering Tullius dies as a result of Skyrim seceding, killing any notion of a military coup. The Thalmor know this and thus encourage the rebellion quietly.
Finally, bear in mind that the current emperor is assassinated by you during the game's events, there is a subtle implication that the one who ordered it has ties to the Thalmor. Tamriel is in the middle of a cold war between the Thalmor and the Empire, with the Thalmor seeking to weaken the empire to a point where their victory can be assured in a war, and the Empire trying to loosen the Thalmor's grip on them in violation of the emperor.
Ideologically, the empire isn't a multicultural society more so it's a federation of nation states that follows an agreed upon set of universal rules (Unfortunately dictated by the Thalmor due to the emperor's lack of spine). Each nation state sticks to their own, maintains their own government and contributes to the welfare of the empire overall through taxation. It is fundamentally a good idea, but is being poorly managed under its current leadership.
tl;dr, side with the Stormcloaks and force the inevitable war early, a war the empire may just stay out of, and a war Skyrim cannot possibly win. Or side with the Imperials and play the long game, in the hopes of a regime change through a military coup and eventual war footing against the Thalmor on winnable terms.