I think any race conspiracy gives power to Nazis and immediately puts Jewish people at more danger. Making both US news and Zionism antisemitic. That's all I've put together.
I really should've asked this in a post long ago, I just feel embarrassed about not knowing.
To add on to this, conflating those two things then gives ammo to actual anti-semites when Israel does fucked up shit. Committing a genocide while saying “We represent all Jews! And we are doing genocide for Jewish reasons!” understandably makes people associate Jewishness with doing genocide.