Do you see any other city with a large population of restless, unhappy nationalistic Dunmer? Ulfric's solution to the social problems in his city is to put them on the backburner. You can criticize that, but the reason is because he's fighting a war on multiple fronts in which the empire is using the Dominion against him. He's got a few things on his mind. Solving the centuries old ethnic issues in his hold isn't one of them right now. It's not racism, it's priorities. Before anyone points to Riften as some panacea, it is also a Stormcloak hold, and the in-game books about it indicate that they had a hard time absorbing a large population of refugees, too.
Mmmm....
Okay, here's proof that Ulfric is racist, and has an agenda...
He relocates people of a differing race and belief system, no matter how well they integrate, into a ghetto, and utilises their differences as a means to reinforce his own position of power...further, he 'tolerates' or ignores, if you prefer, discriminatory and victimising behaviour against those people.
I just wonder how things would look if Ulfric had a railway system...would he have priests of Talos making the selections?