Actually... I find Ulfric to be one of the more reasonable Stormcloaks. He's culturalist, but not necessarily racist. "You're a Nord born into a Cat's body" at worst.
Doesn't really explain the discrimination in Windhelm, though. The Argonians are forced to live in an Assemblage outside of the city, and they're hard workers (in fact, they're made to do work that the Nords don't want to do), while the Dunmer are allowed to live in the city but are constantly harassed and not given help. Any problems for non-Nord citizens are secondary, while Nords are taken care of.
Khajiit merchants are not allowed in cities, other khajiits are accepted, but obviously very rare because of the climate and discrimination. It is similar to the dark elves in the slums and Windhelm. You dont see very many dark elves, because nords hate them. You dont see many argonians, because nords hate them. You dont see many khajiits, because nords hate them.
Dunmer live in Windhelm, Riften, Whiterun, Winterhold, and more. Argonians live "in" Windelm and Riften, and there's a couple in Solitude. The only Khajiit I've seen inside a city is the assassin that's sent to kill you, and I got the impression she had to sneak in (there's also the one in the College, but that's not a city, and it's still a far cry from the number of Dunmer and Argonians you can find living in cities).
The game certainly gives the impression that Khajiit in general aren't allowed inside the cities, not just the caravans.