as far as I know, here's what's going on with them:
1. Ulfric wants to be the high king
Although he can play the part of the humble warrior fighting the good fight for Skyrim, I think he has a power hungry streak and he doesn't do much (IMHO) to dissuade you of the notion becoming High King is a big part of what he's doing .
2. Ulfric wants to protect Nords and their culture but does not care for other races
I think regardless of what is going on with Ulfric he does indeed care for his people and land (well the people that agree with him and don't get in his way at least).
Unfortunately he doesn't really seem to appreciate the fact Nords are no longer the only people of Skyrim (and they weren't the first). The Forsworn, as well as all the members of other races that have immigrated there over the many years Skyrim as been part of the Empire simply make his "Skyrim for the Nords" unacceptable.
3. the other races that came looking for places to stay in windhelm aren't treated very kindly by Ulfric (and are kind of homeless)
True.
4. the Imperials don't really care for the Nords (?) or their culture
I'm not sure I would phrase it like that - they might not especially care for parts of it, but they don't care enough to try and change it. The largely respected the Dunmer's slave owning ways in Morrowind for example, even though the rest of the Empire had outlawed already.
No "don't care enough to change it" is also wrong... the Empire is quite tolerant and, at odds with many representation of long lived Empires in fiction, rather respectful towards its diverse population and its people.
Plus there are a lot of Nords in the Legion, there have been Nordic Emperors etc.
5. the Imperials somehow are infringing on the Nords' right to rule
I guess it depends whether you agree or disagree with the way Ulfric handled the old High King.
6. at some point the Imperials banned worship of Talos
When they signed the peace treaty with the Thalmor that was one of the conditions the Thalmor imposed. The Empire never actually enforced the ban however (so people could go on worshipping, just not as publically), and the Thalmor only got an opening to come in and throw their weight around when Ulfric started making noise about Talos and it looked like the Empire wasn't upholding its end of the treaty..
Plus Talos was a major Imperial deity - his worship was particuarly strong in Skyrim true, but it isn't like the Empire just chose to get rid of some minor foriegn deity who wasn't important to them. They worshipped him to, as one of the Nine Divines.