She named her son Aleph. She has emceed Jewish communal events and been praised for her impeccable Hebrew accent. She made a haunting — and loving — Hebrew-language film of iconic Israeli author Amos Oz’s heart-wrenching memoir, “A Tale of Love and Darkness.”

In a world of celebrity Israel boycotters, from Roger Waters to Penelope Cruz, Oscar-winning actress Natalie Portman has been an Israel backer — even an Israel lover. But her decision last week not to travel to Israel to accept the $2 million Genesis Prize — regarded as the “Jewish Nobel” — has opened up a rift in the Jewish community and is testing the boundaries of what is acceptable criticism of Israel.

Some Jewish leaders regard her decision as “shameful,” scoffing at her explanation that she decided not to attend because she did not want to be viewed as endorsing Israeli Prime Minister Benjamin Netanyahu. Others, on the other hand, said it demonstrated that one can support Israel but not its “destructive policies.”

As the debate raged this week, still others suggested that Portman was giving voice to the growing divide in the Jewish community over the policies of the Israeli government.

“I think it’s a warning sign to the Jewish community — and especially to Israel — of the increasing pressure upon liberal Jews, even liberal Jews who are very supportive of Israel,” said Rabbi Ammiel Hirsch, spiritual leader of the Stephen Wise Free Synagogue in Manhattan.

“It’s a warning that should be taken seriously,” he added.

Rabbi Hirsch described Portman’s decision as “unfortunate,” noting that she had “already agreed to accept the prize when it was offered to her months ago. The reason she ultimately gave as to why she wouldn’t accept the prize didn’t make sense. To accept an award in the presence of the prime minister is not to endorse every action the prime minister takes. The prime minister represents the state. If you get an award, of course public officials are going to show up; what do you expect?”

Portman’s criticism of Israeli leadership — presumably over the recent Gaza border demonstrations and the situation with African asylum seekers— is not coming in a vacuum. It follows that of Ronald Lauder, president of the World Jewish Congress, who, in a New York Times op-ed last month, wrote that the Israeli government was capitulating to religious extremists.

“By submitting to the pressures exerted by a minority in Israel, the Jewish state is alienating a large segment of the Jewish people,” he wrote. “The crisis is especially pronounced among the younger generation.”

And earlier this month, Sen. Ben Cardin (D-Md.), a staunch pro-Israel supporter, attacked Netanyahu at a J Street Conference for his plan to deport African asylum seekers and for using an address to Congress to speak out against the 2015 Iran nuclear deal.

But being the A-list celebrity that she is, Portman’s comments touched a deep nerve in Jewish life and created a firestorm of debate.

The Jewish Insider quoted an unnamed source as saying the Genesis Prize Foundation “went out of its way to accommodate Portman’s concerns about Netanyahu by agreeing that she didn’t have to sit next to him, didn’t have to have him present her with the award and was free to say anything from the lectern she wanted, including whatever critical comments she wanted to level at the current government. However, in the end she insisted Netanyahu not be invited to the event, a demand Genesis couldn’t accept both for contractual and moral reasons.” 

The award was established by wealthy Russian-Jewish businessmen in partnership with Israel’s Prime Minister’s Office and the Jewish Agency. Recipients are asked to distribute the money — the award was raised this year from $1 million to $2 million — to charities of their choice. In announcing Portman’s selection this year, the Genesis Prize Foundation said the money would be donated to Israeli philanthropic programs dedicated to advancing opportunities for women.

In accepting the prize last November, Portman — who was born in Jerusalem, moved to the U.S. at the age of 3, was raised in Syosset, L.I., and attended the Solomon Schechter Day School in Jericho, L.I. — said in a statement that she was “deeply touched and humbled by this honor. I am proud of my Israeli roots and Jewish heritage; they are crucial parts of who I am. It is such a privilege to be counted among the outstanding Laureates whom I admire so much. I express my heartfelt gratitude to the Genesis Prize Foundation and look forward to using the global platform it provides to make a difference in the lives of women in Israel and beyond.”

In announcing last week her decision not to attend the awards ceremony in June — the ceremony was then canceled — Portman said in a statement that she “did not want to appear as endorsing Benjamin Netanyahu, who was to be giving a speech at the ceremony. By the same token, I am not part of the BDS [boycott, divestment and sanctions] movement and do not endorse it. Like many Israelis and Jews around the world, I can be critical of the leadership in Israel without wanting to boycott the entire nation. I treasure my Israeli friends and family, Israeli food, books, art, cinema, and dance.

“There is no question this is symptomatic of a larger problem.”

“Israel was created exactly 70 years ago as a haven for refugees from the Holocaust. But the mistreatment of those suffering from today’s atrocities is simply not in line with my Jewish values. Because I care about Israel, I must stand up against violence, corruption, inequality, and abuse of power.”

Malcolm Hoenlein, executive vice chairman of the Conference of Presidents of Major American Jewish Organizations, said that while her decision as “regrettable, it is part of the climate we see today on campuses like Barnard [College] and elsewhere where resolutions are being adopted that are pro-BDS even though they are likely not to be implemented” by the administration.

“It is the bellwether of a problem that we have to recognize and that we are trying to address. I don’t believe we should continue to play up Natalie Portman as much as look at the issues we are confronting regarding anti-Israel activities that often morph into anti-Semitic activities — and the general rise in anti-Semitism in the U.S. and abroad.”

Rabbi Rick Jacobs, president of the Union for Reform Judaism, referred to the Portman controversy during an address at the University of Maryland on Tuesday. He said he would have attended the ceremony but also recognizes “Portman’s love for Israel. Those who demonize her and question the legitimacy of her views are poisoning the atmosphere.”

“I don’t know if this [action] will be a catalyst for change, but it is an indication that Israelis and American Jews might be more willing to voice their concerns over Israeli government policy.”

Rabbi Jill Jacobs, executive director of T’ruah: The Rabbinic Call for Human Rights, termed Portman’s decision “an extremely powerful and important Zionist statement that one can support the State of Israel and oppose the destructive policies of the Netanyahu government.  … This is the most rightwing government in the history of the country, and it is threatening democracy and expanding the occupation in such a way that it is violating the human rights of Palestinians and threatening the security of Israelis.”

Similar comments were voiced by other left-wing organizations here.

“We’re thrilled she spoke out,” said Rebecca Vilkomerson, executive director of Jewish Voice for Peace. “The more people are willing to talk about these issues publicly, the easier it is for others to do the same — and it is a real indicator of the changing perception of Israel. … We really commend her for her bravery in saying the things she did.”

Libby Lenkinsky, a vice president of the New Israel Fund, said she was pleased that Portman was “using her celebrity platform to say you can love Israel and support Israel and not support all of its government’s policies. … What is important is that she said she loves the people on the ground and doesn’t support the policies of this government or BDS.

“I don’t know if this [action] will be a catalyst for change, but it is an indication that Israelis and American Jews might be more willing to voice their concerns over Israeli government policy.”

On the other hand, Mort Klein, president of the Zionist Organization of America, was critical of her decision, saying “it as pathetic and shameful that Natalie Portman has such a fear of maintaining her status in the anti-Israel entertainment world that she would stoop to issue false and obscene attacks on Israel to benefit her image among her extremist colleagues. … Her statement portrays Israel as worthy of being boycotted, so she aids the BDS movement. Why has she said nothing about the Palestinian Authority promoting hatred and violence against Jews in every aspect of their culture?”

Rabbi Heshie Billet of the Young Israel of Woodmere, L.I., pointed out in a letter to the editor in The Jewish Week that another vocal critic of Netanyahu’s, David Grossman, sat on the same stage with the “democratically elected prime minister” when he received the Israel Prize for literature this year and even shook Netanyahu’s hand.

“She does not support a democratic Israel,” Rabbi Billet wrote of Portman. “She only supports herself … and is unworthy of calling herself a friend of Israel.”

“The more people are willing to talk about these issues publicly, the easier it is for others to do the same.”

Portman was to have been the fifth winner of the Genesis Prize, joining actor Michael Douglas, former New York City Mayor Michael Bloomberg, violinist Itzhak Perlman and sculptor Sir Anish Kapoor.

Dan Mariashin, CEO of B’nai B’rith International, said the award is clearly apolitical and honors those who “serve as an inspiration.”

“To make a political issue out of something that is nonpolitical does not make much sense,” he said. “She said she opposes BDS, but this decision plays right into the hands of the BDS campaign. It has been welcomed as a victory by none other than Omar Barghouti, a co-founder of the BDS movement. … She may not see this as a mistake, but if she is against BDS, one would have thought that she would have seen there would be some in that camp who would welcome it.”

But Logan Bayroff, a spokesman for J Street, suggested that “rather than criticizing and attacking her for listening to her conscience, they should recognize that her concerns about Prime Minister Netanyahu and the State of Israeli democracy and policy today are shared by many American Jews and supporters of Israel around the world.”

Instead of refusing to attend the awards ceremony, David Halperin, executive director of the Israel Policy Forum, suggested that Portman should have accepted the award and voiced her concerns at that time, speaking “directly to the Israeli people.”

“This should be a cautionary tale to those Israelis who are dismissing the growing rift between the Israeli government and Israel from progressives and younger American Jews in particular,” he added. “There is no question this is symptomatic of a larger problem.”