A couple of Dunmer in Windhelm remark that the Nords seem to hate "anyone who isn't a Nord". But none of the other non-Nords in the city seem to share this perception. The Altmer do OK, and the (significant population of) Imperials seem to have quite a high status (Viola, Calixto, Adonato, "the Aretino residence").

Argonians are kept out of the city, yes - but at the behest of the Dunmer, not the Nords. The hatred between Dunmer and Argonians goes far deeper than either group's feelings toward Nords.

UESP lists ten Dunmer people in Windhelm:

Voldsea Giryon - makes no complaints about her treatment, experiences no difficulty or harrassment walking about the city or drinking in Candlehearth Hall.
Aval Atheron - runs a stand in the main market, alongside all the other merchants. Isn't treated noticeably differently from anyone else.
Faryl Atheron - works on a farm, thinks the talk of persecution is overblown, despite firsthand experience of Rolf's harrassment.
Suvaris Atheron - complains (understandably) of harrassment, but works in a trusted position for one of the top Nord families. She also gets harrassed by both sides - Ambarys Rendar repeatedly gives her a hard time about her employer.
Belyn Hlaalu - owns (owns!) his own farm outside the city. Thinks the Dunmer should shut up and work.
Luaffyn - has nothing to say about anything.
Idesa Sadri - also works in a trusted position for a Nord family. Nothing to say about discrimination or politics.
Ambarys Rendar - the most vocal anti-Nord. Not just anti-discrimination, he's actively racist against Nords. When asked about murders in Windhelm, he replies "None of that matters to me. Until someone takes a Dunmer, I let Windhelm deal with its own problems."
Malthyr Elenil - unhappy about living in the Gray Quarter and "rough treatment" (unspecified) at the hands of "Ulfric and his lot".
Revyn Sadri - makes no complaints about racism or discrimination.

So that's two votes for "shut up and work", three for "Nords are bastards", and five abstentions. It's hardly an overwhelming cry for liberation.

Is there racism? Oh yes, absolutely. (Although there's no visible foundation to the claim repeated a couple of times that this extends to all non-Nords.) But while Dunmer seem to be obliged to live in the Gray Quarter (if inside the city), they have no problems moving about the city, running market stands alongside Nord vendors, even owning land and employing a Nord labourer. And although there are some very loud Nord racists (Rolf, Elda), most of the important Nord citizens (the Cruel-Seas, the Shatter-Shields, Captain Lonely-Gale) show them no lack of respect or courtesy. Guards will actively direct you to Revyn Sadri's shop.

Finally, there's the guards. A couple of people complain that you can't get them to take an interest in the Gray Quarter's problems - but then, you can't get them to take an interest in a freakin' serial killer who's murdering Nord women, either, so I think that's more about a general culture of apathy than discrimination. The guards see themselves as a military force, not police - they think their job starts and ends with crowd control.