You're not supposed to like Carol Sturka, so great - the writing worked.
I consider Pluribus to be one the really great shows in the last decade, and I also do not like Carol. Often, I'm annoyed by her actions, and once or twice I was really pissed at how she interacted with the Others, because IMHO, there was just so much unnecessary hostility, or she was just being a dense cunt.
Why would a movie, a TV show or a play require the audience to like the protagonist? Outside of these fictional depictions, I'd probably not be acquainted with someone like Carol - but here, I want to watch her. I want to see how she deals with the overall situation, how choices made by someone who is fundamentally different from me play out, how she grows as a character, how she overcomes her flaws, of which there are many, or how she might completely fail. There even is the option I eventually grow to like her. Wouldn't that be great, an actual character arc?
Carol is an alcoholic who doubts her self-worth and has just lost her love, a death which she directly blames on what she considers to be the alien invaders she now has to interact with on a daily basis. She was also recently promoted to one of the greatest mass murderers in history and the isolation she suffered as consequence of her actions made her realize she really can't exist in complete solitude, leading to a complex relationship with an entity she wants to hate. I think she deserves some jagged edges.
Not so much trademarked, but having a protected origin:
https://en.wikipedia.org/wiki/Protected_designation_of_origin