Along the lines of something like "Why did they assassinate Meir Kahane?"
In each case, the unidentified "they" has been demonstrated to be religious extremist assassins. It doesn't take an vast conspiracy to trigger a religious nutcase. (As an aside: Rabin was the leader of Avodah, a centrist by your definition, when he was assassinated. While I disagree with your assessment of Avodah, this goes a long way to explain why I am advocating for the return of what you term centrism: it was responsible for the greatest advances in negotiating peace between Israel and the Palestinians).
Ironically, considering how little out political views appear to have in common, I completely agree with your assessment of "therein lies your answer to everything": it is the rise of faith based political radicalism on both sides of the West Bank wall that killed the peace process. Assassination of Rabin is but one episode in this decades-long process. Another election in Israel, or West Bank, or Gaza will not have any positive effect on the peace process any time soon. But neither will a war. Or two. Or five.
Both the military and the political efforts to achieve peace have failed. But this is not by any means the end of the story, or the reason to give up. One other path remains, and it has never been tried in earnest. An economic solution. And this solution will require something completely opposite of BDS. Palestinians and Israelis both have common interests as consumers. In fact, those interests are indistinguishable between the two nations. I have a great deal of faith in those common interests to gradually bring the two parties to meaningful cooperation despite all the political forces that tear them apart. Since this will require a great deal of activism outside of the government framework, I see a huge role for peace activists in bringing this kind of economic cooperation together. First, on the humanitarian and private enterprise grounds, but gradually involving business and, inconspicuously, even government interests. Once this cooperation proves beneficial to both sides, it can grow from two economies cooperating for mutual benefit to two states cooperating for mutual benefit. At the risk of sounding too simplistic... bingo! A two-state solution!
I admit, it takes a bit of faith to assume that self-interest can prevail over religious dogma. But we can't forget that both the Israeli and Palestinian societies are secular to a large degree while expressing their respective faiths in a moderate manner. Fanaticism is an exception, not a rule. And we are seeing, particularly in the Abraham Accords, that economic cooperation between religious rivals is a real thing.
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