I actually think that anti-semitism is a serious problem on the left and in anti-zionist discourse.

I don't think it is innately or intrinsically a part of that discourse, but it shows up and is naively or unintentionally enabled and reproduced way too much. That said, no accusation of anti-semitism WRT Israel coming from the right is made in good faith. Not a single one.

Plus I think we need to think seriously about asking the question so defensively and incredulously in the first place. Like, virtually everybody on the left knows that literally every other form of prejudicial discourse is present on the left, even if its presence on the left looks different than its presence on the right, and even if it takes more subtle and often unintentional but definitely unexamined forms. We know there are subtle forms of every kind of racial prejudice, queer antagonism and trans antagonism, classism and elitism, sexism and misogyny, etc. We know that there are problems with all of these things on the left. Why on earth would we possibly doubt that anti-Semitism is also a problem on the left?

In the case of all of these other forms of prejudicial and even bigoted discourse that can be found on the left, we also understand that progressives who are not members of the groups and question have a harder time seeing and identifying the different shapes it can take. We understand that non-black progressives will have a harder time seeing subtle forms of anti-blackness in progressive discourse. That non-trans progressives will have a harder time seeing unexamined forms of trans antagonistic discourse on the left.

So I would say if you are really interested in better understanding this and all of the different potential shapes and forms it can take on the left, you should consider two things.

First of all, you should ask your progressive Jewish friends about it, bearing in mind that if you ask defensively they will probably not speak very candidly to you. But if you ask in a spirit of good faith willingness to engage in honest, self-critical self-examination, they will provide you with many, many, many examples.

Secondly, I would respectfully suggest that you consider that this reflexively defensive incredulity that so often shows up when the subject is brought up is a serious part of the problem. That it is an obstacle to seeing and taking seriously this problem because it prevents exactly the kind of good faith self-reflection that is needed. And a reflexive unwillingness to take it seriously as a problem enables the problem to grow and adapt and even metastasize in our discourse.