When you first enter Windhelm. Everyone but Nord are practically persecuted.
I thought of this as war-time paranoia. Like how the blacksmith in Whiterun(female Imperial) says that the Stormcloaks prefer to buy their swords and armour from Nords - trust issues.
Or any Non-Nord problems are not addressed,
I agree that this prioritizing seems a bit racist, but do you think that Ulfric would do the same in a situation where he DID have the necessary resources?
and it's stated that Ulfric pretty much wants to keep all the Non-Nords in their slum.
Not by Ulfric himself. He seems entirely uninterested in the goings on in the slums of Windhelm. The situation in Windhelm slums is older than this conflict(I believe). It is due to the many refugees from Morrowind. The Altmer in the market square has a very different view on things compared to the Dunmer of Windhelm.
I can definitely see why people would get the impression that Ulfric is racist, but I just don't see "enough evidence to convict". In order for him to be a racist - you have to fill out some blanks yourself.