Hamas is a terrorist group. Israel is a state. State militaries generally have rules of engagement. They define how soldiers are allowed to behave, when they are allowed to shoot or forced to retreat, what is a valid target and so on.
The US was widely criticized for its military's civilian death toll during the invasions of Afghanistan and Iraq as well as the occupations thereafter. Rightfully so, in my opinion. But the US military - like most state militaries - had explicit limits and for every target the US military command defined the acceptable number of casualties. You wouldn't bomb a busy market with families and children to kill one Taliban soldier for example.
Israel also has rules of engagement and limits on civilian casualties. The difference is that if the US had used the same numbers during its occupations, Iraq and Afghanistan would be depopulated. And any US soldiers doing what is permissible in the IDF would be court martialed.
> This is a war, Israel is not responsible for the Palestinian population beyond following the rules of war, which they are.
The rules don't apply to Israel (nor the United States for that matter - nor Russia): https://asp.icc-cpi.int/states-parties
Also
> Israel has every right to do everything within its power to stop them.
This contradicts the idea that they have to "follow the rules of war", whatever that is supposed to refer to. You can either claim they're adhering to whatever international laws, treaties or conventions you think they're adhering to or that they're allowed to do whatever is in their power. These two claims are mutually incompatible.
Also
> This is a war
What is? When did the war start? October 7? Was it not a war when Hamas was launching rockets before October 7 and the IDF were bombing civilian buildings they declared to be "used by Hamas"? Who are the sides of this war? Israel and Hamas? Then WTF do you call what's happening in the Westbank? Also you do realize that "Hamas" is both a terrorist group and the official administration of Gaza (and that it was "elected" two decades ago and there haven't been elections since and most people in Gaza were either not born or not old enough to vote at the time)? And you're aware that there are other Islamist terrorist groups operating within Gaza such as the Muslim Brotherhood and that Hamas has no control over them (i.e. is unable to negotiate ceasefires on their behalf)? Heck, what is the goal of the war?
According to Netanyahu, Israel wants to end Hamas and any threat to Israelis once and for all. This not only mirrors the rhetoric he used against Hezbollah (before withdrawing from the war in Lebanon) but is also completely open ended and undefined. At least when the US invaded Afghanistan they had an explicit end state (ousting the Taliban) - as insufficient as that goal turned out to be when they exited (and the Taliban returned). Heck, even Russia had a clearly defined goal when invading Ukraine (several, actually, some contradictory but most of them very much well-defined and not open ended).
Israeli state media and Israeli politicians have at numerous times framed this "war" as an ethnic cleansing (i.e. removing Palestinians from Gaza and expelling them from the territory of Israel). I guess at least that's a well-defined goal with a clear end state compared to Netanyahu's rhetoric.