I think you're conflating "Karen" with "entitled asshole". There are tons of entitled assholes in this world and "Karens" are just one type. As another commenter mentioned, "Karen" is used for entitled, soccer-mom-types, especially for treating front-line workers like crap and attempting to get a manager for their demands. As for the right-wing association, I don't think being right-wing is inherent to being a "Karen". I think that association was borne from the current political climate and viral videos.

It's like how in elementary English class they teach that all words ending in -ly are adverbs, but not all adverbs end in -ly: All "Karens" are entitled assholes, but not all entitled assholes are "Karens".