I only ran into a handful of stormcloaks that we today would consider truly racist. I also think that when you're talking about truly separate races (not just dudes who happen to have a different skin color), it's not so out of the ordinary to have an in-group preference of sorts. Especially if you live in a harsh and unforgiving land like Skyrim.
That said, in this case what I have seen more from the stormcloaks is dislike of "provincials". That is it isn't your race that they have a problem with; it is that you are a relative newcomer to their land and do not ascribe to (or sometimes even respect) their cultural norms and traditions.