What Karan writes is "Father would never allow me to marry a commoner, much less a poor Dunmer miner." It's far from clear that "Dunmer" is the deal-breaker of those three words.
Racism is endemic in all factions in Skyrim. I've already talked about Ambarys Rendar. The Thalmor are way bigger racists than any Nords, as a brief conversation (almost inevitably followed by a brief fight) with any of their patrols will remind you. The Forsworn hate the Nords, Dunmer hate the Argonians and vice-versa, the Imperials think they're better than everyone, nobody trusts Khajiit, and the stronghold Orcs won't even talk to you unless you do some dangerous-yet-menial errand to show that you're "their friend" first. Wherever more than about three people of the same race gather together, they will find some common cause against everyone else. The Nordic racism is prominent solely because there are so many Nords in the setting.
A major part of the background storytelling is devoted to the story of Ysgramor's extermination of the Snow Elves, the latter's degradation into the modern Falmer, their equally bitter conflict with the Dwemer, and current mindless hatred of basically everyone. The Argonian invasion of Morrowind, the Great War, the Markarth Incident - basically, almost all the lore that's been added since Oblivion is about either race wars or outright genocide.
Within that "endemic racism" framework, is there really any reason to suppose that the Stormcloaks are systemically "more racist" than everyone else? Are there racist Stormcloaks? - yes, of course, but there are non-racist ones too, and conversely there is racism on the Imperial side as well. But everywhere you go, racial minorities simply aren't particularly downtrodden. The only race that's really widely discriminated against are Khajiit, and the Stormcloaks don't treat them noticeably worse than Imperials do.