Give them work as I would to any Nord. That goes for the Argonians, Khajits and actually everyone. Any racial discrimination would be punished in public, to set an example. I would want to achieve a restored, strong Skyrim for the people (be it Nords or non-Nords) not a bickering, warring Skyrim which collapses on itself due to men, mer and beast folk can't set aside age old conflicts and differences. Look at where the Dunmers ended up after centuries of interior conflicts, xenophobia and oppression and/or persecution of the "lesser" races. That's exactly where the Nords are heading if Ulfric wins and keeps his current attitude and views.
But some DO work/have jobs. Even shops/bar. Why do people only see the empty half of the cup? Have you ever considered that some might be, oh, I don't know....
lazy? Yeah, big shock!
Also, we don't know for sure that discrimination from the citizens of Windhelm against the Dunmer is not punished. Maybe it's just not presented in-game. I personally take what the NPC's tell me with a grain of salt, people are biased and tend to present only
their side of the story.
And Ulfric should definitely start acting baby-sitter and go around town chastising the naughty citizens, I really see him doing that...

In our world, in real life, how many acts of injustice happen, some even go unpunished. Have you never been insulted or taunted or even threatened? Can you tell me that IRL every single one of these get punished?
It's society...these things happen. The leaders cannot be held responsible for every insult another citizen throws around.
But I do agree on what you said about the bickering and setting aside old conflicts, especially in these troubled times.
Also, on the "punish in public". Being a leader is a sensitive matter. Sure I would love (if I were a leader, let's say) to go around and smite injustice. But you have to be careful about these things. Going all mighty and smity(not a word, haha) against some to appease others might not turn out so nice in the long run. You have to find a balance, being a leader and keeping the respect of all your people is not such an easy job.
It's not exactly like Ulfric does anything about the racism and even violence against the Dunmer population of Windhelm, either. Maybe he has a good reason (like other concerns, or ignorance of how bad the situation is - on the other hand, the proprietor of the New Gnisis Cornerclub claims to have tried to talk to him several times, being ignored), maybe he just doesn't care. Maybe something changes I haven't found out about yet.
Do we have clear proof that he does nothing about racism? From where/who? I'm asking because maybe I missed something...But I wouldn't base that accusation solely on what the Dunmer of Windhelm say.