Internally, denying humanitarian aid is seen as the legitimate and time-honoured strategy of "sieging the enemy state" though not all agree on how legitimate that is (I'm sure you can see the strangeness of sending food and medicine to enemy soldiers). Certainly supplying the enemy with fuel to use in their rockets, vehicles and armaments is seen as foolish (even if that would also provide fuel for the hospitals whose fuel was stolen by Hamas). There is zero desire in killing non-militants (outside of few extremists), but given the extremely horrible inhumane atrocities committed by Hamas (e.g. https://en.wikipedia.org/wiki/Sexual_and_gender-based_violen... ), the acceptance of collateral casualties is higher than usual (and Israel already went extremely out of its way to minimize civilian casualties before the Oct 7 attack). Hamas' tactics that intend to maximize the deaths of their own civilians are also a contributing factor to that acceptance. If you believe there is genuine desire or action specifically to kill civilians outside of that then you believe in fake news.

In terms of non-homicidal genocide (i.e. genocide in the sense of dismantling the group without killing its members), certainly a lot more people are fine with something like a Transfer plan (for example, I've heard a proposal that Egypt will take Gazan Palestinians as refugees/civilians and similarly have Jordan absorb the Palestinians in Yehuda and Shomron) and don't see it as much of an atrocity, merely taking back the land those Arabs conquered and colonized starting at around 640AD, without actual harm to those individuals (in fact, their lives could be much improved!). There's also the fact that Israel is very tiny; Even from just the southern part of Gaza, Hamas already fires rockets at Israel's most populated cities, giving them the mountains of Shomron (incidentally, the capital of the Israeli kingdom), simple mortars could rain down on Israeli civilians without warning and could easily lead to an actual genocide of all Israeli Jews, so moving the people a few tens of kilometers east sounds like a peaceful resolution in comparison.

Naturally, there's also the element of a long conflict. Arabs have been killing Jews in Israel during the British Mandate as well as the Ottoman rule of the region (in fact the IDF traces its roots to what are essentially local militias the Jews had to create to defend themselves). Israel's scroll of independence (a document that is considered that closest thing Israel has to a constitution) actually includes two paragraphs calling for the Arab nations surrounding Israel to work together in peaceful cooperation, so literally the very first action Israel took as a state was to call for peace, and literally the first thing that happened in response was an attempt to destroy Israel. After 76 years of war, certainly there's lowered sympathy for the enemy, especially one that elected Hamas (see above) and rejected peace (I've somewhat recently learned that outside of Israel almost no one knows that the Annapolis Conference very nearly resulted in peace via a two-state solution that was refused by Mahmoud Abbas [which I've heard he has later come to regret, not sure how reliable that is]).

Rising anti-semitism around the world (especially how popular it is to call for a genocide against Israeli Jews is in the form of the "From the river to the sea" phrase) also creates a backlash - Israel must act strongly to defend itself since it is the only place in the world where Jews can be in charge of their own fate and their own defense. If the BBC publishes lies about what happens in Israel, and protesters in England are calling for a genocide unopposed, not only should we not listen to what the English want us to do, we should prioritize ourselves even further. This is why IMO something like BDS is counter-productive, it only causes further resentment and defiance in Israelis; If you want peace between Israel and Palestine you should instead work to make sure Israel feels safe enough to be able to relinquish territory to the Palestinians without having another October 7th instead of working to undermine Israel (unless your goal is the destruction of Israel of course).