The instant someone makes that accusation, I disengage. I’ve learned the hard way.
People think that calling someone antisemitic (or anti-Muslim) is a great debate tactic if you’re trying to put your opponent on the defensive and derail the conversation. There’s a major difference between criticizing a government/organization and general bigotry, and they know that perfectly well, but people who want an easy, emotional argument don’t care. They’re not interested in details.