Can a person of any race be called racist for denigrating another person of the same race?

This question was generated from another question asked.

Personally, I don’t believe so. As the article provided in the above question pointed out: “It’s intended to be provocative, offensive, and even insulting, but it’s not a racist term.” This was in response to a specific insult but I think that it goes for any statement where the insulter and the insultee are of the same race, even if the insulter is full of self loathing.