Extreme voices tend to drown out everyone else. I mean, what type of reasonable person has the energy and will to involve themselves in this toxic quagmire, right? The type of people willing to do so are strongly biased to people with Very Strong Views.
Trying to organise a protest around unfocused nuanced views is hard. "Free Palestine" is easy and straight-forward. "Hamas is wrong, but Israel should offer a solution for the people of Gaza that does not involve a de-facto concentration camp under military control" doesn't really fit on a billboard.
And lets also be realistic: yes, "both sides" have blame, but "both sides have blame" does not mean "both sides are equivalent". The people of Gaza are by and large powerless, and have been for a long time. The initiative for any solution really rests primarily on the Israeli side, who have been controlling much of life in Gaza for a long time now. The situation in Gaza and that Israel has never seriously offered any solution is frankly just disgraceful, and could only have ended in violence one way or the other sooner or later.
That's only true if you view the "Israeli government" and "Hamas" as the only sides that exist. That is not the case; you don't need to choose either of them.
Now, of course it's true that everyone has legitimate grievances here for all sorts of reasons, an it's also true that forever banging on about every little thing anyone has ever done wrong will lead to another 100 years of suffering. But that doesn't mean we (broad international community) can't and shouldn't try. Even if it fails, I think it was worth the effort to try.