All in all... the Thalmor is enemy to all who aren't Thalmor.
What is the Dragonborn?
The Dragonborn is the personification of the sacred pact between Alessia and Akatosh, in essence, a pact to keep the Mundus on going. The Thalmor see the Mundus as a prison, and a return to the pre-creation state to be an escape. Others assert that the pre-creation state was a prison, and the Mundus is a necessary step to become something even greater. Shor/Lorkhan failed deliberately to show how not to fail, and Talos actually succeeded.
And the Thalmor just hate the fact that a human beast succeeded at that. The Thalmor have have mythopoeic tall poppy syndrome, basically.