I believe that "Karen" was coined as a very specific descriptor to identify White women who use privilege and entitlement to unapologetically exploit BIPOC in public. The White male equivalent of this would be "Kyle."

It isn't intended to be a blanket indictment against all people who happen to have those first names (as you pointed out with your example of Karen Bass).

The onus was still on the person who wielded the term "Karen" against your friend -- to highlight/validate WHY the accused party was allegedly acting like a "Karen."