It can a daunting task for that minority kid to approach the white kids -- especially when none of them extended an invitation and in certain circumstances, made it very clear in every single way except for verbally, that You Are Not Welcome.
Works both ways. Living in one of the blackest cities in America-- Philadelphia-- one might think black people would be more comfortable approaching white people and extending an invitation. It's never happened, to me or to anyone I know here.
For whatever race, it's simply a lot less exhausting to be around people with whom you don't have that issue.