In regards to whether Ulfric's cause is just or not, I am finding the matter a little complicated. I know that Ulfric treats those of other races with little regard unless they can prove themselves to him. He kind of has a "you have the burden of proof since you aren't a Nord like us" mentality. However, I don't think what he does as jarl says to much about his cause as a whole. I don't think other jarls would have to enforce the same racial segregation he does.
In regards to my own opinion, I find secessionist movements quite alright,. It's within peoples rights to self-governance. However those movements can also be even more difficult to pull off than revolution. Ulfric seems like a pretty convicted person in what he does. Do you think he did what he did seeing no other feasible options? Or do you think he is essentially power hungry and has no regard for others opinions, whether they want independence from the empire too ect. I have read relevant lore text "The Bear of Markath: The Crimes of Ulfric Stormcloak" by Arrianus Arius, and also worthy of note is game dialogue with Jarl and high king Torygg's and then Jarl Elisif' court wizard Sybille Stentor. Stentor, who had direct contact with Torygg seemed to indicate that he had a high opinion of Ulfric and was willing to listen to his case for independence. But instead Ulfric when met again challenged him to a dual to the death.
I am apt to say Ulfric was in the wrong. What do you say? Can you make a convincing case to me?