I can really only speak for myself, but I think atheists may lean toward whichever side will offer the best chance at peace, through reason, logic, practicality, and realism.
Although I have immense sympathy for the people of Gaza, and I understand their point of view; as such that it has been misguided by the poison and brainwashing of Hamas, and the false promises of 'victory over the Jews' in 'end-times' as stated in one of their prophecies, it appears their demands are self-defeating, unrealistic, and void of reason.
Beyond the Palestinians 'wanting' the Jews to vacate the land, and not caring how such a thing would even be possible, and beyond them feeling honored at the idea of sacrificing their own children as martyrs for the cause, they should instead ask themselves, 'If we lived in a house on that part of the land instead of this part of the land, what would we want, next?'
If the answer is 'a better life' and freedom, they need to then ask themselves how, exactly, they would define those terms. Once they establish exactly what they want for their lives, perhaps better schools, better job opportunities, the freedom to move around as they please without being hassled at checkpoints, and so on, they can then begin to think what would have happened if Hamas would have used the hundred million dollars they wasted on building tunnels and buying missiles, and instead poured that money into the Palestinian economy, and actually used it for good instead of evil.
If they want freedom, they need to stop blowing people up, which would be the first step in the right direction of joining and finally being recognized as part of the civilized world. They will need to come to terms with the reality that Israel is here to stay, and proceed from that point forward - with calm negotiations, and the ultimate goal of living peacefully side by side.
Israel, on the other hand, is caught between a rock and a hard place. Part of why they are being targeted by suicide bombers is because of the built up hostilities and frustrations that the Palestinians have to suffer on a daily basis when they pass through the checkpoints. Yet, if the checkpoints were eliminated, there would undoubtedly be more suicide bombers blowing up civilians in Israel. But if the need for the checkpoints (suicide bombers) were eliminated, the checkpoints would eventually be eliminated, as well.
From what I see, not just currently, but from the beginning of Zionism, both sides have enough hatred-with-good-cause for the other side to last a trillion earth-lifetimes. But we can't change the past, and like it or not, we need to share this world, and that means living next to each other on the same land.
I see and believe wholeheartedly that Israel is willing to do that - they want peace, and they can be reasoned with. Palestine, however, I see as a desperate, screaming, unorganized, spiteful and unrealistic 'kill kill kill' mob-mentality religiously fanatical people, who would rather see their own children being blown up than to sit down at a table and ask for reasonable and realistic terms as part of a peace negotiation.
I am on the side of peace.