The danger is that by introducing the threat of civil or even criminal charges against those who are accused of being antisemitic under this strict definition, it will have a chilling effect on freedom of speech and academic debate/inquiry.

You should read this opinion piece by the lead drafter of the IHRA definition itself, talking about the dangers of Trump's 2021 executive order (essentially what this latest bill is proposing to enforce by law). In it he warns about the definition being weaponized, saying:

Starting in 2010, rightwing Jewish groups took the “working definition”, which had some examples about Israel (such as holding Jews collectively responsible for the actions of Israel, and denying Jews the right to self-determination), and decided to weaponize it with title VI cases. While some allegations were about acts, mostly they complained about speakers, assigned texts and protests they said violated the definition. All these cases lost, so then these same groups asked the University of California to adopt the definition and apply it to its campuses. When that failed, they asked Congress, and when those efforts stalled, the president.

The real purpose of the executive order isn’t to tip the scales in a few title VI cases, but rather the chilling effect. ZOA and other groups will hunt political speech with which they disagree, and threaten to bring legal cases. I’m worried administrators will now have a strong motivation to suppress, or at least condemn, political speech for fear of litigation. I’m worried that faculty, who can just as easily teach about Jewish life in 19th-century Poland or about modern Israel, will probably choose the former as safer. I’m worried that pro-Israel Jewish students and groups, who rightly complain when an occasional pro-Israel speaker is heckled, will get the reputation for using instruments of state to suppress their political opponents.