DD1 is at a school which is fairly culturally diverse. I think it's about 30-40% ethnic minorities, and there are lots of girls from other European backgrounds, as well (I'm not sure you would count them as being from an ethnic minority, although they are from a cultural minority).
At first, when she would mention a name, I would usually have no idea whether that person's family was of African origin, or Asian, or European. (None of Tilly, Jennie, Rochelle or Francesca are white European, for example.) It was never an issue to her, and isn't to me.
She isn't one of the "cool" girls in the class, but is quite pleased that she speaks to all the girls in the class at least once a week, for one reason or another (different classes, clubs, catching the same train, etc.)
She has been invited to the houses of many of the girls, and meets up with them for outside school socialising. This includes girls of all different cultural backgrounds.
DD2's and DS's schools are less culturally diverse, but both have close friends of other ethnic backgrounds. Those children are certainly not "left out", although they are part of a cultural minority within the schools.