This is an interesting and informative discussion.
When it comes to categories and self-identity, there is caution in labeling those who identify differently as lacking consciousness or being culturally unaware. As has been noted in this thread, these acceptable or unacceptable identities are socially constructed and therefore vary by context.
I liken it to the ongoing issue of Black "versus" African American that has existed for generations. There are those who identify as Black and there are those who identify as African American. There are also those who identify as both and neither. Identifying or not has implications for not just yourself but also for your group identity and representation where such categorical distinctions are "needed."
I acknowledge and identify as both Black and African American (and as a part of the African Diaspora that spans across countries and continents) and fully know the history and relevance of both. And I say "fuck off" to those who think they can question anyone's level of awareness and consciousness based on that.