I don't think the libtard left really cares about Palestine, and they don't really push the issue from what I can tell. Or if they do, they don't get a lot of MSM coverage. Ilhan Omar has talked about it, but no wonder given that she's Muslim. Otherwise a few lefties who see racism everywhere might correctly see it in Israel, too - a broken clock and all that. Then, there are some oldschool lefties who didn't forget the old slogan that Israel is an "imperialist bridgehead", which used to be a cold war framing in the context of West vs. USSR. But mostly, it seems that the prominent libtards/democrats are very silent about the issue. The MSM consensus is "support Israel" all the way.
As for the conservatives, it's almost as if unconsciously they know exactly that their own anti-Woke rhetoric clearly and logically leads to questioning the Israel narrative, which is the mother of all weaponization of victimhood, moral blackmail and group identity thinking. But instead of "going there", they go like "no no sir, I know my conservative stance implies criticism of Israel, but I'm a good boy and support Israel!"
Definitely messes with people's heads so that they can't think straight, which weakens them.