If she's actually mistreating or offering customers of another race lesser service - than yeah, complain to management. But if she's treating them equally, I don't think there's any reason to complain to management... saying, so and so doesn't like me anymore because she's racist and she doesn't like my boyfriend is really not something management can fix. Flat out telling the coworker that you're hurt by her behavior should be done... but I doubt it's going to make the coworker see the light.

I know I have friends that live in the middle areas of the country that are convinced racism doesn't exist and are shocked by it... while living in mostly caucasian areas... But I think because they see less of people of other races they don't have the same stereotypes. I remember being surprised at some of the race breakdown of the states that were for Obama vs. clinton or McCain - he had strong support in some predominantly white areas of the midwest.