There are actually 2 distinct conflicts in Israel. It's important to distinguish them.
War with Hamas is not what will determine the future of the region
On the eve of the current violence in Israel/Palestine, something extraordinary was about to happen. For the first time, a new Israeli government was going to be formed dependent on the support of an independent Arab party: the Islamist Ra'am, led by Mansour Abbas. The coalition that would have supported that government would have been extraordinarily broad, ranging from the far left to the far right, united only by the determination to end Benjamin Netanyahu's tenure as prime minister. And while the architect of the coalition was the centrist leader of the Yesh Atid Party, Yair Lapid, the prime minister would initially have been the right-wing leader of the Yamina Party, Naftali Bennett.
I don't know which is more remarkable, that Abbas would have accepted Bennett as prime minister, or that Bennett would have accepted depending on Abbas' support. But for a moment, there was agreement.
Then the violence broke out. First in Jerusalem, where protests against the prospective eviction of Arab families from their homes in East Jerusalem led to violent clashes with police. Then in mixed Israeli cities like Lod, where Arab rioters torched synagogues and businesses, and Jewish vigilante groups harassed and attacked Arab residents. And, finally, between Israel and Gaza, as Hamas fired rockets at civilian targets within Israel and Israel's military responded with air strikes.
I believe it is impossible to understand the current violence without the context of that prospective coalition agreement. For the same reason I believe that even if we shortly see a ceasefire with Hamas, moving beyond the violence within Israel will ultimately require getting those same parties or their equivalents back to the table.
The world is primarily focused on the conflict between Israel and Gaza, since that is where the worst civilian casualties have been felt. But those casualties are the result of war between Israel and Hamas, and Hamas is not "the Palestinians." It is a distinct organization with its own agenda as well as the party governing Gaza, and has been designated as a terrorist group not only by the United States and Israel but also by the European Union, Canada, Japan, and many other states and organizations, most recently the Organization of American States. The latest war started when Hamas began firing rockets, which it did not in hope of achieving any kind of military victory but to provoke an Israeli response and thereby to win a propaganda battle. It doesn't make the loss of life any less terrible, nor does it let Israel off the hook for its settlement policies or for the way it prosecutes the war, to be clear about what Hamas' aims are in fighting.
But the conflict within Israel's cities is of a very different character. It was spontaneous and unorganized, fueled by viral social media but rooted in deeper grievances. Some of those grievances are explicitly related to the occupation of the West Bank and the encirclement of Gaza, but many are related to the inferior status of Arab citizens within Israel: In terms of funding for social needs and economic development, which has always left the Arab sector shortchanged; in terms of relations with the police, who are rarely present either to keep the peace or fight organized crime, but who respond swiftly and repressively to protest; and, most fundamentally, in terms of representation in government.
Part of Hamas' motivation in launching its attacks was precisely to lay claim to those grievances; to declare, in so many words, that it is the only defender that Arab citizens of Israel truly have. The extreme right within Israel has been eager to agree, which is why mobs of Jewish settlers from the occupied territories have traveled to cities like Lod to beat up random Arab residents. Caught in the crossfire are those, like Mohammad Darawshe, who have been persistent advocates of coexistence and peaceful change. That's not an accident; it's the goal.
The question is whether it is the goal of Israel's government, or of those who would lead its government. In particular, the question is whether Naftali Bennett wants to distinguish himself from the hooligans, or whether he wants to associate himself with them. Does he see Israel's Arab citizenry as a fifth column working for an enemy that must be suppressed? Or does he see them as a segment of the electorate with whom he disagrees about deep ideological questions but whose legitimate grievances deserve to be addressed within the political system? Does he aim to be the prime minister of Israel? Or the prime minister of Jewish Israel?
In the wake of the last war in Gaza in 2014, Bennett took to the pages of The New York Times to call for a "bottom-up peace" built not on Israeli withdrawal but Israeli expansion: Not only expansion of settlements, but expansion of investment in the Arab sector and expansion of the scope of Israeli law and of citizenship rights to more Arab residents in the territories not under Palestinian Authority control. It is easy to ridicule such an agenda as both fanciful and unserious. But taking it at face value for the sake of argument, it clearly depends on cooperation for success — specifically, cooperation from Arab Israelis and their leaders. Indeed, it's hard to credit any kind of good faith to that agenda if that kind of partnership — the kind presaged by a possible coalition with Abbas and Ra'am — isn't being actively pursued.
Far from building bridges over the ruins, though, Bennett has burned what few bridges he had built. Abbas has quietly made it clear that he would be ready to resume coalition negotiations once the fighting was ended, and has reiterated that Jewish-Arab cooperation was an end in itself, and not merely a means to an end. Bennett, however, quickly declared that a change coalition was "off the table" because Ra'am, being an Arab party, could not be relied upon to respond to the violence. Meanwhile, his colleagues are building different kinds of bridges, not between Jewish and Arab citizens, but between factions of the Israeli right. Netanyahu is now reported to be in talks with Gideon Sa'ar of the right-wing New Hope Party, who had sworn never to serve under him, and also with Benny Ganz of the centrist Blue and White Party, who had made similar pledges (and had previously broken them). If either party comes to an agreement with Likud, Bennett's Yamina will surely join as well. In consequence, the most likely outcome of the current violence is the reunification of the Israeli right.
There would be a certain logic to that outcome; Israel has plainly had a right-wing supermajority for years, albeit one divided over Netanyahu's leadership. But it's a logic with dire implications for Israel's future. Unity against a foreign foe can paper over many deeper problems, but can also be a source of strength. But "unity" built on antagonism to a portion of the citizenry promises only more violence to come. It would be ironic but also depressing if a reunified Israeli right wound up responding to the rockets from Gaza by giving Hamas precisely what they want.