I've seen a few anti-racism policies in my time. I've signed them for companies I've worked for, associations I've joined, I've approved one or two for my own businesses and even helped write one when I worked in Compliance.
I have never once seen a need for, or a policy with any such caveat as the one insisted upon by Labour supporters. There's just no need for it, the two issues are entirely separate. Bringing in the caveat shows that in their eyes, the two issues are somehow linked.
So let's say Labour take the definition as is (despite those unworthy Jewish groups also being against it, for the reason that they feel it conflates legitimate criticism of Israel with anti-Semitism). And then someone in the Labour Party (likely on the left) makes a legitimate criticism of Israel. What will happen? The people in the party against Corbyn will start foaming at the mouth, calling for action against those members because "well, we as a party have accepted the definition as written! This IS anti-Semitism!" So then they have to turf out members for no good reason or, not take action against them and have the faux outrage warriors (who are motivated primarily by being anti-Corbyn) dominating the next media cycle for Corbyn's failure to combat anti-Semitism.
They're just not the people I'd rely on to create the most relevant definition. You want a definition of antisemitism? Ask the organisation whose prime responsibility it is to fight it. You should know you'll never get 400% agreement from any large group of people - you can find exceptions in any group.
What you've found is a list of groups who are already motivated towards a certain cause, trying to insert that cause into another one. That they share the same heritage is of no relevance. If there's a group of the size and profile of the IHRA whose primary goal is fighting antisemitism and who don't have the ulterior motive of fighting the Israeli government's foreign policy, who disagree with the definition - let's talk about them.
I'll say it again, the wrong type of Jew. The only Jewish people allowed to be listened to are those who take any criticism of Israel as anti-Semitism, and anyone who contradicts them, even if they are Jewish, are anti-Semites.