So yeah, this is derived from the thread asking whom we support in the Imperials vs Stormcloaks war.

The question which appeared was "Why do the Thalmor even ban the worship of Talos?"

I found myself just as curious, so I've made some research.

Prepare for a lesson of TES history, which is more or less accurate and shortened by a lot, to make it understandable.

Answer:

Because he's not one of the Divines.

Tiber Septim (a.k.a. Talos) ascended into godhood just before his death, as a God of Manhood and War, and "became" a divine deity, in a way, thanks to his deeds. He conquered entirety of Tamriel and, thus, began the Third Era, under rulings of the Septim dynasty. When referred to deities, people refer to The Eight and The One. Where the Eight are the eight original deities and Talos is the one who is not a deity from the start, but a mere mortal.

Aldmeri Dominion claims that a mortal cannot become a divine, therefore the worship of Talos is an offense to the remaining eight deities and should be eradicated.

Thing is, that Tiber Septim appears both in Oblivion and Morrowind series and is presented as a god there (through some interesting quests).

I've tried searching some more on this decision, and that's what I've found:

The Altmer that formed the Third Aldmeri Dominion are actually an extremists and nationalists. After they've conquered Valenwood, which was allied with the Empire, they severed all ties with the Empire completely. When they set their eyes on Elsweyr and recreated The Elsweyr Confederacy, the Empire had no choice but to respond, what led to more and more intense conflicts and eventually The Great War, which was temporarily suspended by signing the White-Gold Concordat. The Empire and the Dominion are currently in state of a "cold war", but the radical Altmer plan on overthrowing the Empire completely and finishing its rulings. And since Talos was an Imperialistic hero and champion, it is imperative to crush his image as a deity between the Imperials.

The fact that the Altmer, apart from the Champion of Cyrodiil, had the greatest impact on saving Cyrodiil during the Oblivion Crisis doesn't help the Empire at all either. Summerset Isles, Altmer homeland, was long occupied and administrated by Imperial legions, under the rulings of the elder council. Since the Empire was weakened after the Crisis, and Altmers were at power, they drove the Imperials out of the Summerset Isles, established an independent Dominion and are now seeking to conquer the Empire which ruled over them for so long.

In other words, one of the main factors here is revenge and lust for power.