Hawley is many things but I don't know of any evidence that he's anti-Semitic.
Look back at some of the things he said around the time of Janet Yellen's confirmation hearings. In my view and that of many others, he was not-so-subtly invoking "cultural Marxism" talking points that have their roots in anti-Semitic conspiracy theories.
"Cultural Marxism" is not anti-Semitic.
It may not be in common parlance, but its origin is in a conspiracy theory about Jewish critical theorists destroying Western values or whatever. I can't help but feel that the Ivy League-educated Hawley would know about these implications and not describe a Jew with those terms unless he was intent on that connotation.
Just because a phrase has offensive origins does not mean that everyone who uses it intends to reference those connotations. In Hawley's case, I suspect he assumes that A) The term doesn't have anti-Semitic connotations for most listeners, and B) Those who accuse him of anti-Semitism will be relying on a tenuous and obscure connotation that will weaken their argument and make them look oversensitive. This is a clever strategy, and it will continue to work until leftists can learn to pick their battles.