It seems that originally it ('Karen")was a tool for silencing women who abused their white privilege in a way that men did not seem to do. If that is true, then it is something that needs to be addressed rather than pretending it doesn't exist.
We call on all men to change toxic masculinity. Perhaps all women need to change toxic femininity rather than say there is no such thing.
Sadly it has evolved into a criticism of women who complain much more than necessary and make a fuss about nothing. It has become a popular term because many people recognise that woman. Do they recognise her because they are misogynists or because she exists? Do they recognise her because the world allows men to complain as much as they want and silences women?
In some ways it is like the term cock-lodger, although 'Karen's' genitals are not referenced. That is a sexist term. It is a vulgar sexist insult. But it is a sexist term we are happy to use because it describes a type of man most of us are very familiar with. Why didn't we just use the already insulting term that was applied to similar women: gold-digger? Perhaps it wasn't rude enough.
It is like another MN classic: man-child. Once again a useful term. We all know what it means and that it is not good. But why reference gender? What was wrong with child? Are there no woman-children? If so we never hear about them.
But a thought for the OP. Consider not reporting if that would bring misery to your son. Boys have never liked tattle-tales and being one attracts bullying. I imagine that having a mother who is a tattle-tale could attract bullying too. Sometimes of course we have to do things that correct, challenge or even provoke bullies. But if so, your son is the one you will be bullied, not you.
Like you I think the racist picture is appalling and you dealt with that in a way you thought appropriate. I think you dealt with it well. But more importantly, does your son agree? Or would he like to take it further? This isn't just your decision. It is also his. Of course, you as the adult have to guide him. You have the final say, but it is his world and he has to live in it. What does he think?