No no, the Thalmor wants the Civil War to stay a Civil War. Both the Empire and Stormcloaks are pawns to them. Whether or not either side wins, the Thalmor are hurt pretty badly.
In any case, the Dumner of Windhelm...now talk to the High Elf and she'll say something in the lines of "I've proved myself to be a hard worker and worthy of living in Windhelm so the Nords don't really bother me. The Dumner, if they swallow their pride and actually help the Nords and prove themselves to the Nords, then they'll be better off."
Ulfric gave the Dumner a home and the only reason they're living like crap is because the Dumner aren't really doing anything to prove themselves. Nords are a group of people who respect honor and tradition. Not to mention that in troubled times, racism is brought out. Just look at America right now. A lot more racial problems going now than in the 1990s.
As for Khajiit not being allowed in Windhelm...well it's for their safety as well as the Nords. Literally NO races trusts Khajiit so it's in everybody's interest if they just stay in tents.
At least the Empire is aware of this and they clearly don't like it. In fact I'm pretty sure that they're the next target for the Empire if they quell the rebellion in Skyrim. The Stormcloaks are oblivious by comparison.
Except the Dunmer don't really see the point in proving themselves. Yes it's stupid, but it's not exactly on their list of priorities considering they just had their homeland destroyed and their way of life ruined. They're looking for a place to live, not honor, respect, or friendship. What they're asking for from the Nords is to be left alone. Not preferential treatment. They have jobs, opened businesses, and they're willing to work. It's not like they're svcking on the teat and not giving anything back in return. And for the Altmer, she still has a home to go to, and as far as we now, the Altmer population in Windhelm is barely in the double digits, compared to an entire refugee community.
I agree with the Khajiit part though. Sad really.