To remain in office, the government might also need to retain the parliamentary support of Raam, the Arab Islamist party, which is seeking greater rights and resources for Palestinian citizens of Israel, who form about 20 percent of the population.
For some, the leftist, centrist and Arab constituents of the putative new alliance would have only a limited effect on Mr. Bennett and other right-wing members.
“They’re all fig leaves,” said Diana Buttu, a Palestinian citizen of Israel and a former legal adviser to the Palestine Liberation Organization. “We may see a softer, gentler outward face. But I’m fairly certain that the policies are going to remain the same, if not worse, under Bennett.”
Others were more hopeful that an equilibrium would be maintained. Some said the likely appointment of a center-left minister to oversee the police force might encourage officers to exercise more restraint, following several controversial police actions in recent months that contributed to rising unrest in Jerusalem.
For ultra-Orthodox Israelis, or Haredim, the putative new coalition is troublesome because it would be formed without the involvement of either of the two main Haredi parties, who have participated in most coalition governments this century.
But for others, that was cause for qualified celebration.
Anat Hoffman, a campaigner for a more pluralistic approach to Judaism in Israel, did not expect the coalition to last its full term, nor for it to significantly weaken the control over religious affairs currently exerted by Orthodox rabbis. But she hoped it might create a more tolerant atmosphere that would show “there is more than one way to be Jewish, and more than one way to be an Israeli, and more than one way to be an Israeli patriot.”
“This is a huge thing for us,” said Ms. Hoffman, the executive director of the Israel Religious Action Center, a group that advocates religious pluralism. “To have a normal government without, every day, one of the government members coming up with a more extreme sweeping initiative that rocks our whole country.”