You would have to work with their past actions. And then it becomes non trivial to define "anti-semite".
So it is not really about "what does the word mean" but "how do you decide who fits the definition and who doesn't". People are concerned about this because it is very hard to make a law that 100% only fits to the people you want to target (leaving asside wether the principle is correct or not).
What in the fuck are you even talking about? Do you have the same issue identifying a racist? Do you need to MRI scan a KKK members brain to be sure if they are racist, do a deep dive into the background? Goddamn some of you on lemmy are fucking stupid...