How should this be achieved without war and a genocide-like event? What are people that are in favor of Anti-Zionism specifically hoping for?

Israel is composed of people who just went through a legitimate holocaust and genocide themselves. Therefore it seems logical to most people that they'd be ready and willing to exact vengeance in the measure it was dished out to them. Furthermore, their Tanakh (our Old Testament) details the battles between the Children of Israel and their neighbors, which were murderous, atrocious, and genocidal on both sides. Why should modern warfare be any different?

Conversely, Palestine is composed of an amalgam of pan-Arabic people and, correct me if I'm wrong, no particularly deep roots in terms of common ethnic descent, or claim to such land or territory, since it was British until recently. Therefore, the Palestinians are a stand-in for all the Arab world, and by proxy, we're fighting all those Arab terrorists by targeting Palestine, and vice versa. Now the Arab world is nakedly genocidal against the Jews. They really make no bones about their desire to wipe Israel from the face of the Earth. By proxy they did a pretty good job during WWII -- the Third Reich, being the enemy of their enemy, was greatly pleasing to the Arab world.

So the Middle East has two little Davids fighting each other on behalf of their respective Goliaths. Israel's campaign has finally ramped up to the point where the rest of the world cries injustice and genocide and enough. But Israel has vowed "never again [to us]" while living under very real and existential threat that the entire Arab world would very much do it again to them, if they had half the chance.

So if the West puts the brakes on Israel, then we're letting the other Goliath's David win, and nobody around here wants that.