I can't get myself into being a Stormcloak supporter unless I am playing a Nord. It just doesn't feel right. While on the other hand I can accept the idea of a Nord supporting the Empire.
I do believe that maybe not so much the other human races, but Beast races and Mer seem to be looked down on in general by the Stormcloaks and their supporters.
You think so? My first character was a Dunmer mercenary/hitman and he joined the Stormcloaks. First off, he's of Hlaalu descent, an therefore supported the Empire. But when the Empire fell apart and Morrowind was invaded, he felt that the Empire had betrayed his people. He fought for his life against the Lizards and were one of the last to flee for Solstheim.
When he came to Skyrim, he was met by Imperials trying to kill him. Having two causes now, he went on a personal war against the Imperials. Of course, this eventually got him both beaten and imprisoned, so he looked for allies.
When he saw the poverty in the Grey Quarter, he decided he wanted to help these poor Dunmer. So, when he already was hunting Imperials, he might just as well join the Stormcloaks. And he also figured that he could use the influence he gained from being a commander in the Stormcloak army to appeal to Ulfric. And as I roleplay, I play that Ulfric bent a little to his will, granting the Dunmer better lives.
You can justify anything with some imagination.