It implies that the only reason a Jewish person could object to extremely strident criticism of Israel is because their own Jewish identity is tied to the Israeli state. This is, at least occasionally, criticism that takes insufficient care to actually associate itself with the current Israeli government or their military leaders, rather than Israel or Judaism in general.
As an illustration, I appreciate that there is a way to argue that the whole ‘from the river to the sea’ thing is not anti-Semitic but that plenty of Jewish people who whole-heartedly disagree with the treatment of the Palestinian people nevertheless find it threatening. If someone chooses to use that chant anyway, I would consider that they flat out don’t care about offending Jews who would be on their side. For me, criticising a Jewish person who is offended by fairly scattershot abuse of Israel is uncomfortably close to victim blaming. If there’s going to be an actual solution to the whole Palestine thing, then offending moderate Jews is the exact opposite of the way to find it.