Mr. Ohana, for his part, has accused the liberal camp of hypocrisy. In a Facebook post before the November election, he wrote that many gay leftists were sending him images from nearly 20 years ago of Mr. Ben-Gvir and Mr. Smotrich at the “Beast Parade,” asking if these were going to be his future coalition partners.

Mr. Ohana noted that the last government, a broad coalition of anti-Netanyahu forces, included a small Islamist party, Raam, which is virulently opposed to gay rights.

Reflecting the layers of complexity in Israeli society, Mr. Ohana related a story of how warmly he, his partner and their son had recently been received by the rabbi and congregation of an Orthodox Yemenite synagogue they had visited in Jerusalem.

The rabbi, Mr. Ohana recounted, blessed their son in the traditional way, naming the two fathers in place of the more usual father and mother. “The congregation,” Mr. Ohana wrote, “with a good-hearted smile on their faces, responded with a loud ‘Amen!’”

Gabby Sobelman contributed reporting from Rehovot, Israel.