These conversion mavericks, several of them bastions of Israel's modern-Orthodox mainstream, are not the only thorn in the rabbinate's side at the moment.
An organisation called Hashgacha Pratit is challenging the rabbinate's monopoly on kashrut certification, by which all restaurants and shops claiming to be kosher are required to have rabbinate supervision and pay rabbinate inspectors. Created by restaurant owners out of frustration that rabbinate supervision is too expensive and too limiting in terms of the products they are allowed to use, Hashgacha Pratit is more lenient, and keeps the cost of supervision in check by using a combination of volunteers and staff paid on a fixed and transparent pay-scale.
The religious establishment eyes Hashgacha Pratit with concern. Charedi politicians have even initiated legislation to stop it in its tracks.
In marriage too, there is something of a rebellion going on. A small number of Orthodox rabbis are defying the law and officiating marriages that are not registered with the rabbinate. And among the majority who still marry through the rabbinate, growing numbers are choosing to organise their wedding through Tzohar, instead of turning to their local rabbinate office.
An alliance of Orthodox rabbis, Tzohar says that many rabbinate offices handle marriage registrations from the public in a way that turns them off religion, and offers a parallel track. As a result of pro-Tzohar political pressure, the rabbinate has been forced to ratify these marriages.
Scandals are not helping the rabbinate's public image, among them the fact that the last Ashkenazi Chief Rabbi, Yona Metzler, resigned amid corruption allegations in 2013, and in February was indicted for fraud, bribery and other charges.
The opposition of the current Chief Rabbis, David Lau and Yitzhak Yosef, to allowing Charedi men to be drafted into the military, has earned them some unpopularity among the general public.
Rabbi David Stav, who competed against Rabbi Lau for his post in the 2013 election, promising sweeping reforms in the rabbinate if chosen, said that the rabbinate faces a serious crisis.
"It's more than just credibility - it's something very deep," he said.
The issue, he believes, comes down to how the rabbinate views the public. He said: "Do we treat them as customers or as a captive audience?" Rabbi Stav, who chairs Tzohar, claims that the rabbinate today regards the public as a captive audience, and as such has become complacent.
"Whenever someone gets a monopoly and is not facing competition, there is no initiative for them to improve themselves," he argued.
"The air that is needed to breathe in a democratic society is competition."
Rabbi Stav does not want to see the rabbinate dismantled, but rather to see internal competition introduced in almost all areas. He would like to see different local branches of the rabbinate competing for custom, whether in marriage registration or kashrut supervision.
The Chief Rabbinate's defenders say that its critics are mistaken in their push for decentralisation. "They don't understand the necessity for central authority," said Shlomo Aviner, one of Israel's best-known non-Charedi rabbis. "You need central authority in an army, you need central authority in politics and you need central authority in religion." Rabbi Aviner, head of the Ateret Cohanim yeshivah in Jerusalem, is dismayed by the new conversion court, believing that its religious standards are too lax and that "there are some things that depend on the authority of the Chief Rabbinate and the question of who is a Jew and who is not isn't something that every rabbi can decide".
What is more, he thinks that the purported need for the court is not genuine. The court's initiators say that around 300,000 people in Israel moved there from the former Soviet Union or were born to parents who made the move but who are not Jewish, and they urgently need access to straightforward conversions. Rabbi Aviner, however, is convinced that most have no interest in converting.
According to Rabbi Stav, if the rabbinate does not make conversion accessible "someone has to ask what has gone wrong". Rabbi Aviner insists that the facts that conversion numbers are small does not reflect badly on the rabbinate. "The Jews of Russia are not interested in conversion," he said. "They feel very good in their situation now - they don't feel any lacking from the fact they are not Jewish."
Rabbi Aviner also thinks that "generally, there are no problems with the rabbinate". Scandals pertain to isolated cases, and most Israelis get what they need from the rabbinate, he said.
Jeffrey Woolf, an expert on religion in Israel and an historian at Bar Ilan University, expects the Israeli rabbinate to survive - but not without changing.
"I don't see the rabbinate leaving so fast, but the degree of its authority in different areas will change," he said.
Initiatives such as independent conversion and private kashrut will, he predicted, eat into its strength.
He commented: "In many areas I think we're looking at a restructuring and a watering down of the authority of the rabbinate."
