“Both of us are Jewish from the ‘wrong’ side,” said Ms. Vilenchik, 25, meaning their fathers are Jewish but not their mothers.

The couple rewrote their seven blessings “to be more secular, without God, God, God all the time,” Ms. Vilenchik said. Some secular brides also break a glass, a ritual traditionally performed by the groom. Ms. Vilenchik chose not to because she was in heels.

Pola Barkan, 28, director of the Cultural Brigade, a group that promotes Russian culture in Israel, married Mark Barkan, 29, in an Orthodox Rabbinate ceremony. After his family had fought to remain Jewish in the Soviet Union, Mr. Barkan said he would not give up on it so easily. Still, Ms. Barkan insisted on adding an eighth blessing, praying for all her friends to be able to marry without exception or exclusion.

Rabbi David Stav, the chairman of Tzohar, an Orthodox organization that helps couples navigate the Rabbinate bureaucracy, said, “Every monopoly needs competition. I think the competition will be good for the Rabbinate and improve it.”

Batya Kahana-Dror, the director of Mavoi Satum, a group that helps women who have been refused a Jewish divorce by their husbands, also facilitates private, unregistered Orthodox weddings.

“It’s a civil revolution,” Ms. Kahana-Dror said. “The young religious public is very critical of the Rabbinate. Today there are options. People are voting with their feet.”