I agree. I hire people frequently in my position, and if I see an overtly political job on a resume I tend (maybe unfairly) to assume the applicant’s personal beliefs align. If this particular politician is an extremist, it’s likely future employers will be making assumptions about you. It isn’t fair to do so, but hiring decisions are made by humans, and humans are assumption-making masters.
Also- if you strongly disagree with your employer, you won’t be giving it your 
effort and might not even get a great recommendation from it.