Chinese, Korean, Ethiopian and similar orphans would be identified as minority members. I doubt that a Ukrainian born adoptee or a Moldovan adoptee with an English name would be identified as any sort of minority member.
As I understand it, while some White people will adopt Black babies, they are far less likely to adopt older Black children that have been taken away from their parents by social services people. I base this on what I have read in the Miami Herald. There are a lot of such children in foster care, and not all of them are appear to be members of some "minority".
I have a friend who adopted a Taiwanese girl. When he and his wife go out with her, some dimwit always has to say something silly, like "What a beautiful child! She's adopted, isn't she?"
Duh!