I was just reminded of another word that might come closer to what you're asking, although you should be very aware that this is a strongly negative word that is deeply entangled with some very politically difficult American racial history and you should be very careful about using it because it could offend people.
The word is minstrelsy and it refers to the 19th century minstrel shows that were based on stereotypes of African American behavior that today we would regard as shockingly offensive.
In modern times, the word might be used it in a couple of situations:
As a very strong criticism of a movie, TV show, or other performance that relies on extremely stereotypical characters or ethnic stereotypes. If you describe a movie as indulging in minstrelsy, then you're saying that the Black (or other ethnic) characters are so one-dimensionally stereotypical that the movie is garbage and the author is probably a racist. As I said, it's very strong criticism where you're deliberately intending to insult the author.
If you are member of a minority who hears someone say something that you think is racist, you might respond by acting in a stereotypical way specifically for the purposes of making them feel bad. Later, you could describe your own behavior as "performing minstrelsy" or "descending into minstrelsy." Once again, this is a very strong word, and you'd only use it if you're trying to describe behavior that is very vicious, and certainly not if you're just joking around.
This word is still associated mostly with African American stereotypes, but it can be extended to other minorities as well. Here is an example of an article that uses minstrelsy to criticize a show for trafficking in gay stereotypes, and another one using it to criticize the Canadian Prime Minister for trying too hard to "act Indian" while visiting India.