Whether it's appropriate to reference Karen may be a tricky question if you're new to the topic, so here's a handy ABC decision tool.
A. What's the subject of your story?
Go. Karen is appropriate to use as a name in these contexts.
Stop. It is not appropriate to use "Karen" in these contexts. Try a thesaurus for better words.
B. What's the purpose of your story?
Go. Treat Karen like any other name, avoiding jokes, publicity stunts and double entendres at the expense of the subject.
Caution. "Karen" should be used only with quotation marks to differentiate it from the identity and with deliberate effort to discourage conflation with the identity.
Stop. "Karen" should be used in this situation only when it is the actual name of an involved person/ethnicity/place etc.
C. What's the tone of your story?
Go. Use Karen just like you'd use any other personal name or ethnic identity.
Caution. Any usage unrelated to a specific person or entity named Karen should be placed in quotation marks to differentiate it from the identity Karen, and context should clarify that this usage is socially unacceptable.
Stop. Avoid passe, inaccurate & harmful stereotypes.