Dagmar
Defender of the Bunnies of Skyrim
This has no support in the lore. It's simply a popular theory because it's based on something Michael Kirkbride wrote. Kirkbride is probably the largest and most influential writer/contributor to the lore of the Elder Scrolls universe. However, he was neither an employee of Bethesda nor retained by Bethesda to come up with this portrayal of the Thalmor (Bethesda used him as a freelance writer for the lore after he and the game publisher parted ways many years ago), and it was never been adopted by Bethesda as lore. As such it's nothing more than an interesting observation of where the lore might have gone regarding the Thalmor if Kirkbride was still with Bethesda and overseeing the development of the lore of the Elder Scrolls universe.I'll explain it again in spoiler tags.
The Thalmor's goal is to destroy the "towers" that separate Mundus from Oblivion/Aetherius because they believe that by doing so they will "be with the gods." The Great War wasn't actually about the elves believing that Talos isn't a god, they know he is a god. The very reason they started the war was because they knew. Their goal is to halt the worship of Talos, because by doing so this would make him cease to exist. The Thalmor are using the entire issue of of Talos worship to further their goals. Their first goal is to destroy Talos, which will be accomplished somewhat by making worship illegal. Secondly, it weakens the empire as a whole because it started the civil war.
Only the empire is losing troops in the civil war. The Dominion wants this. They started the civil war by planting Ulfric as a sleeper agent to do just that. If the empire wins the war, the Thalmor gain because the empire lost troops doing it. If the rebels win, the Thalmor gain because the empire lost troops and the entire nation of Skyrim, which is a fatally crippling loss. But the best scenario for the Thalmor is if both sides lose as many men and women as possible, making the empire and skyrim weaker when the next war begins.
The only way to "win" is to minimize the number of casualties and keep the empire as strong as possible. That means NOT losing Skyrim. If the empire loses, the elves win. If the elves win, mundus will be destroyed, because the entire goal of the Thalmor (and thus the Dominions) is to destroy the towers that keep mundus existing away from Oblivion, and by them defeating the empire they will inevitably accomplish that goal.
Thus, if you know all of this, it is impossible in good judgement to side with the rebels, because doing so only furthers the Thalmor goals of weakening the empire and eventually destroying mundus.
The rebellions goal of legalizing Talos worship again is a good one to be sure. However, the moment the Dominion declares war the White-Gold Concordant (which prevents the worship of Talos) will be void, thus assuring Talos worship continues.
Thus, in the war between the empire and the dominion is actually a war between saving and destroying mundus. The dominion already has an advantage on the empire, in order to save mundus everything must be done to strengthen the empire. Even a united empire couldn't win against the dominion the first time. The empire has already lost a significant portion of its power by losing the provinces. The only way to save Mundus is to keep the empire as strong as possible so that it can defeat the dominion and stop the Thalmor from destroying mundus.
Thus, when looking at the BIG picture, especially from the point of view of the Dragonborn (who goes on a quest to save the world, siding with the empire is the only correct choice. Siding with the rebels helps doom the world. Siding with the imperials helps save it.
The elderscrolls.wikia.com is an extremely unreliable lore resource and this is a perfect example of why it's so unreliable.EDIT: Also, straight from the horse's mouth
"Fate
Ulfric can be killed during the Civil War if the Dragonborn chooses to side with the Empire. After the Battle for Windhelm, the Dragonborn storms his throne room, and he requests that the Dragonborn will kill him, as "it will make for a better song". Upon death, he can be encountered in Sovngarde as a specter, interestingly regretting his belligerent actions against the Empire due to how it only weakend Skyrim and strengthened the Thalmor"
Taken from elderscrolls.wikia.com
Ulfric's remorse has nothing to do with weakening Skyrim and strengthening the Thalmor. If you go to the actual source (Ulfric in Sovngarde) rather than rely upon a mediocre lore resource like that website you would know that he expresses remorse over the fact that the civil war created an abundance of souls of fallen Nord warriors from both sides wandering the fields of Sovngarde for Alduin to feed upon, empowering Alduin in a manner that wouldn't have been possible if Skyrim was at peace (something which Esbern warns both him and Tullius about during Season Unending). That's the actual reason why he is remorseful for his part in the civil war. It has nothing to do with a non-existent realization that he weakened Skyrim or strengthened the Thalmor.