A big thing a lot of people miss in this false equivalence is that Saudi Arabia isn't the only Muslim-majority nation in the world whereas Israel is the only Jewish-majority nation in the world. Is that something that should matter when pointing out the nation's atrocities? Of course not, but to a lot of people, it absolutely does. That's how things like harmful Jewish tropes getting associated with the nation turn into these big deals alongside other such uncarefully worded criticisms. A common sentiment among my Jewish family is "those Muslims can just go somewhere else, we Jews only have one place that doesn't want to kill us" and this is far from a rare thought. It was similarly hammered into me from a young age, albeit not as harshly as some of my Orthodox relatives who have had a much harder time breaking out of it.
If there was literally one more Jewish-majority nation in the world, you wouldn't see this weaponization of Jewish identity, at least not to the same extent, and why it doesn't really work the same with Islamophobia being directly tied to criticism of specific nations unless you extend it to ALL such countries (and don't get me wrong, there's plenty of Islamophobes that do that).