For some reason, I'm bad with every single person considered a hawk.

Literal

For-some-reason hawks [quotative-と] regarded people [topic-たちが], every-single-one not-good-at.

鷹派 ('hawk faction') is the standard Japanese political term for hardliners, mirroring English's hawk/dove distinction. 目される ('to be regarded as') is a formal passive. ことごとく ('each and every, without exception') is a literary adverb that emphasizes totality — stronger than 全部 or みんな. The final 苦手 is a bare predicate without copula, characteristic of casual introspective speech.