I highly doubt those protestors actually give a fuck about the Palestinians, Gaza, or the occupied West Bank (besides the fact that Israel itself is an occupation). They just want the hostages back and don't like Netanyahu.
But the media is gonna spin this as though it's just "bad apples" like Netanyahu that are the problem and if they were removed it'll be all good.
Instability to the Israeli state is good. The war has caused a ton of instability in the economy due to mobilization.