Maybe that's my bias, but that seems to be a very... specific way of sorting sides.
Mind if I rephrase that?
Pro Israeli side, which includes people who care that the hostages be saved. Some also want a 2 state solutions implemented.
Pro Israeli control of Palestinians side: people that believe any Palestinian autonomy will result in a repeat of the Oct. 7th massacre, partly because of the, well, Oct. 7th massacre.
Pro Palestinian side, which includes people who believe Israel should be destroyed and Jews killed, as well as people who maybe don't want want Jews killed but care that Israel is defeated and/or Palestinians are not bombed.
I'd say both phrasings are about equally accurate and objective.