And we know this type of thing works because we see it everyday with US internal propaganda. The last thing the US needs is an adversary with a direct line to the US populace controlling what they see. Also, I'm not even talking about misinformation, just pushing what stories are seen and not seen. Once you add in misinformation and bots it's pretty wild how easy it appears to control the population.
The point is not to push Americans towards Israel or Palestinians, the point is to push Americans apart from each other, so that each half of the political divide sees the other as supporting baby-murderers, as people you cannot be friends with, compromise with and shouldn't even try to talk to.
I am not exaggerating, each of these things I have seen being explicitly pushed.