I think you overinterpret what she says. She complains that the Stormcloaks are suspicious of her, like they think she's going to poison them "or something" (it's been a while since I asked about it, but I'm pretty sure her words goes something like that). It's not exactly an active campaign to force her out of business. The blacksmith, Adrienne, also complains about the Stormcloaks being suspicious, but since she's married to a Nord they at least will shop from him.

Belethor (Breton) and Carlotta (Imperial) doesn't seem to have any trouble with the Stormcloaks (well, Carlotta always has trouble with men, but that's not related to business). I don't think I asked the wood elves (at the meat stall and at the Drunken Huntsman).

So, yes, there is suspicion and xenophobia among at least some of the Stormcloaks, but I wouldn't exactly say that they actively try to force non-Nords out of business. (Note that there are several non-Nord traders in all cities, Windhelm included.)