Karen is accepted slang as the term for a type of unpleasant middle aged white woman. I think people can distinguish between people they know named Karen and the stereotype.
Just as (mentioned) John.
As well as Dick has negative connotations, but I certainly do not assume any Richard I meet is a terrible person because the nickname is slang for something else. Same with a "right Charlie" or other names.
I understand how people named Karen (or Dick etc) can be tired of the association, hopefully it will become dated and fall from use.
Yes, it may be similar to other names, like John or Dick, but the use of Karen seems quite different. John or Dick can be applied to any male that fits the description. They can be of any age or race. That doesn't make it right, but it is quite different.
Karen is used to describe someone of a specific race, age group, and sex. That makes it not just derogatory, but as
@CrazyPanda stated, racist, ageist and sexist, which moves it closer to a hate category. The sexist is less of an issue, because just as John and Dick would only normally be applied to a male, Karen would only be applied to a female, by definition.
There are lots of women (and men) that are outside the specific demographic but that otherwise fit the stereotype of the typical "Karen", as used in the epithet. However, they for some reason are excluded, because apparently only older, white women can be overly-entitled, obnoxious, and loud. There lies the crux of my argument against the comparison to other generic "names", and my intense dislike of the use of the name in the first place.