Usually Karen = behaviour or attitude, right?
Nope. It has to do with sex. Go search for "Karen" on Reddit, where it originated, and then search for any other name you like, and find any name that is supposed to be raped, abused, suxually humiliated, taken down etc. just as much as "Karen". Please post back here with the name(s) and the link(s) proving your points.
Usually Rat = pest or vermin, right?
Nope. It has to do with animals. Go search for "Rat" on google, and then search any other animal name you like, and find any animal name that is supposed to be exterminated and poisoned just as much as "Rat".
That's the logic of your argument applied to a different context in the hopes you see how little sense it makes and how little relevance it has.
Rat = vermin. Rats are also animals who display certain behaviours (although we use it to describe certain types of humans too). The majority of animals do not fall under the definition of vermin.
Karen = entitled. Karens are also women who display certain behaviours (although we use it to describe certain types of men too). The majority of women do not fall under the definition of Karen.
This is like trying to auto-ban the word idiot because it's synonymous with 'stupidity' under the guise of ableism. Can you use idiot to be ableist? Absolutely. Is that wrong? Yes. Can you also use idiot for anyone displaying idiotic behaviour without being ableist? Also yes.
If my dd's teacher called her an idiot because she's dyslexic, through no fault of her own - ableist.
If I call my dd an idiot because she got into a fight at school she could have walked away from - well... no. She's behaving like an idiot.
And as for the errand you've ordered people on... I'm not sure what you're hoping to prove with that? Other than there are vile humans on the internet? Incels exist on reddit? None of that is news nor does it justify auto-censoring it on Mumsnet.
I am seriously invested in arguing this point because MN auto-banning the word Karen above everything else is... well it's sending a message. A very clear message.