I mean...they hate the empire, but they worship an Imperial Emperor
Tiber Septim was an Emperor. Talos is a god. And the Empire in 4E 201 is not the Empire of Tiber Septim OR of Talos
They may hate the current Empire or not, it's not really relevant. What is relevant is that they want to secede from it and rule themselves, so they can be free to worship Talos, or Tiber Septim if you so choose, because under the rule of the current Empire they are not allowed to do that.
If the Stormcloaks are hypocritical for wanting to break away from an Empire in which it is illegal to worship a former Emperor that has become a god, then what does that make the Empire who agreed to repudiate his divinity and make it a crime to worship him?
they hate any species not Nord,
And your proof of this is? I mean, aside from stuff that is also common or general policy in Imperial held territory, or just the words and actions of a couple of angry drunk losers.
but Ulfric is trying to get rid of the Empire
No, he's trying to secede from the current Empire because the Empire that was "prevalent" in Skyrim for all those years no longer exists.
as Hadvir's father says at the beginning of the game
He's not Hadvar's father.
when asked about the Empire - "Nords are no fairweather friends").
Unlike the Empire, which abandoned one of their own Divines, who as noted above is also the apotheosis of their greatest Emperor. And who were also willing to give away part of Hammerfell in order to appease the Dominion, and then cut all ties with Hammerfell when the natives objected to being sold off to ensure Cyrodiil's short term safety.