There are quite a few examples of ulfric's racism, the figurehead of the stormcloaks.
To start with, can't remember where I found this out but its bound to be on one of the elderscrolls wikis, when Ulfric came into power he forced all of the dunmer to live in the grey quarters slum, as well as making the argonians live outside the city walls.
Also if you talk to brunwulf he will say about how he tries to talk to Ulfric about improving the quality of living for the dunmer in windhelm and that ulfric will not deal with it, that ulfric thinks that there are only two kinds of people "nords and the people below them"
Spoiler I know that Brunwulf replaces ulfric if you choose to go with the imperials, but he states that he never wanted to be jarl so he doesnt really have any reason to make it up. Also when he becomes jarl he talks about undoing the racism caused by Ulfric
IIRC the Dunmer refugees came to Windhelm in the wake of destruction of Vvardenfell and the Argonian invasion of Morrowind, and were given that section of the city in which to settle. That was almost 200 years before the events of Skyrim (the game). Ulfric did not force them to live there, since they have been living there since long before he was born.
With regard to the Argonians, if you speak to Brunwulf about it after he becomes Jarl, he states that he will not allow them into the city proper either. They will still be relegated to the docks "for their own safety." The only difference between Brunwulf's "Argonian policy" and Ulfric's is that the game allows you to ask Brunwulf about it and he is allowed to state a reason. You never get to have the same discussion with Ulfric, so you can believe what you like - but there is no reason NOT to believe that Ulfric kept them out of the city for same reason as Brunwulf.
Going back to the Dunmer question, you blast Ulfric for forcing them to move into the Gray Quarter (which - again - he did NOT do)... but Brunwulf states no intention to allow them to buy city property outside of it. He only talks about taking meetings to discuss making improvements in the Quarter at some future time, because he expects to have money and resources to do that now that the war is over. That would be the same money and resources that Ulfric
didn't have when he was Jarl, money he couldn't spend on anything, including the Gray Quarter, even if he wanted to, because fighting and winning the war is and must be his first priority.
Having played both sides to the finish, as far as I can see the only difference between Ulfric and Brunwulf that is verifiable through actual dialogue spoken by themselves and that is not tainted by the subjective opinions, biases, or outright ignorance of other NPCs... is that Brunwulf intends to discuss making improvements in the Gray Quarter with the money he will have that Ulfric didn't have and therefore couldn't spend on the Gray Quarter or anyting else. Dunmer? Still segregated. Argonians? Still segregated.
Honestly after all the hype about Brunwulf, I was not impressed.