Not all Israelis are Likud, and not all Palestinians are Hamas. The problem is not the 'sides' being 'mean' to each other (quotes used because I think your choice of language trivialises the atrocities being committed by both sides), it is the civilians who are not part of Likud or Hamas being dragged into it.

The entire situation in Israel / Palestine is primarily a tale of escalatory tit-for-tat, and politicisation of hate, all starting from a relatively small initial grievance. Netanyahu showed himself when he deliberately provoked conflict in 2021, causing harm to civilians on both sides - in that example, it was blatant how willing he was to cause this much suffering for such a selfish reason, but that boldness only comes because Likud has been doing the same thing only slightly more subtly for years. So when Hamas commits war crimes, it was predictable that Likud would treat it as an opportunity to commit a bigger war crime and try to genocide the Palestinians in Gaza.

Neither Likud or Hamas want an enduring peace - their entire political relevance is through escalation. But the way to get peace is not by further escalation of violence / war crimes. The best way out of this is for the people of Israel and Palestine to say no to Likud and Hamas respectively, and pick leaders who want and know how to de-escalate.