Barely four months after the political earthquake of the January 22 Knesset elections, Israeli politics are about to undergo another seismic shift. This one will bring less drama, but it just might have a deeper impact on the system.

The catalyst is Arye Deri, the onetime Haredi wunderkind and convicted felon, who returned on May 2 to the chairmanship of the Sephardic Orthodox Shas party that he founded years ago. Within days after his installation, Deri initiated a series of high-wire maneuvers to reposition the party, long considered a pillar of the right, as a moderate force on the center-left.

His moves aren’t subtle. On May 8, a senior Shas lawmaker close to Deri, former cabinet minister Yitzhak Cohen, wrote a letter to Prime Minister Benjamin Netanyahu, urging him to embrace the 2002 Arab Peace Initiative. Under Deri’s predecessor, Eli Yishai, Shas was firmly within the right-wing, pro-settlements camp. Deri is a dove.

On May 13, the party’s spiritual mentor, Rabbi Ovadia Yosef, signed an agreement to share control of the country’s Chief Rabbinate, a longtime Haredi stronghold, with theological moderates of the Religious Zionist-Modern Orthodox movement. The deal lets Shas name the candidate for Sephardic chief rabbi, while the post of Ashkenazi chief rabbi goes to a prominent religious moderate, Yaakov Ariel. Left in the cold is the Ashkenazic Haredi leadership, long the dominant force in Israeli Orthodoxy.

Later that same day, May 13, Deri himself announced an agreement, previously considered all but unthinkable, to enter a “dialogue” with the ministries of finance and education over reforms in the independent Shas school system. Finance and education are both controlled by Yair Lapid’s Yesh Atid party, which vowed in its election campaign to slash funding of Haredi schools that don’t teach the government’s core curriculum — math, English and science. Deri announced that the new agreement would suspend the cuts, allowing time for a dialogue on curriculum reform.

Education Minister Shai Piron, a Lapid ally, issued his own statement shortly after Deri’s, announcing that Haredi schools would be submitting to government curriculum rules. The leading Ashkenazi Haredi rabbis had been railing against the core curriculum for months. Now the largest Haredi party was ready to adopt it. Piron called it a “historic evening.”

On the surface, Deri’s moves look like a win for Yesh Atid. They bring the largest Haredi party a big step closer toward integration within the broader Israeli society, one of Lapid’s top goals. They open the door to liberal reforms in the rabbinical establishment that controls marriage, divorce, adoption, conversion and burial — major concerns of Lapid’s secular, middle-class constituency. They bring new pressure for renewed peace talks, an overlooked Lapid campaign promise.

But the package is a mixed blessing for Lapid. Shas’s acceptance of the moderate Ariel as Ashkenazi chief rabbi shuts out an even more liberal candidate, Rabbi David Stav, who is favored by Lapid and most other secular politicians. The rabbinate deal also scuttles legislation that would have weakened Shas’s control of the 150-member Chief Rabbinical Council, which chooses the chief rabbis. The bill would create a majority for Stav by adding 50 new members, including women for the first time. Now it’s dead.

Besides angering progressives, the compromise embarrasses Lapid’s close friend and ally Naftali Bennett, head of the religious-Zionist party, Jewish Home. Bennett supports Stav and favors the council-expansion bill. Most of Bennett’s party went behind his back to close the deal with Shas.

Most important, the education deal infuriated Lapid’s base. Hostility toward the Sephardic Haredi party is a visceral reality among Yesh Atid voters. Lapid got hit with a flood of criticism after Deri announced the deal from supporters who accused him of coddling Shas.

The next morning, May 14, Lapid issued his own announcement, claiming there was no deal and calling Deri a liar. The cuts in Shas school funding weren’t canceled, he said, but merely postponed for six months. The reason wasn’t a deal with Shas, he said, but a legal technicality: The government couldn’t defund a school system if the children had no alternative, since the state is obliged to provide an education to every child. There’s a new public Haredi school system being planned, but it’s not open yet. When it opens, Shas schools will get defunded unless they adopt the core subjects.

In fact, all this was made plain in Deri’s and Piron’s statements from the night before. But Lapid’s broadside gave him useful cover. He’s still learning to think like a politician. Much less useful for Piron, who now had to issue another statement backing up his boss, in effect calling himself a liar.

If all that sounds Machiavellian, it’s nothing compared with the Shas endorsement of the Arab Peace Initiative. The Arab plan calls for a Palestinian state with borders based on the pre-1967 cease-fire lines and a capital in East Jerusalem. Israeli acceptance would likely mean immediate withdrawal from the coalition of Bennett and his settler-backed party, dissolving Netanyahu’s majority.

The prime minister could theoretically replace Bennett with Shelly Yachimovich’s Labor Party. But that would put Netanyahu on the right flank of his own government, a status he wouldn’t accept. Shas’s embrace of the peace plan solves that problem. That makes it harder for Netanyahu to say no.

This brings the prime minister that much closer to a decision he’s never wanted to make. It also brings Shas closer to reclaiming seats in the Cabinet, with all the ministries, perks and patronage that have been the party’s life-blood for decades.

Contact J.J. Goldberg at goldberg@forward.com