Dorit Raviv, an American Israeli, plays with her sons, Amit, left, and Edo, on March 29 at a basketball court near their home in Mevaseret Zion, west of Jerusalem. (David Vaaknin/For The Washington Post)

— For many American Israelis, binational life is the best of two worlds. They travel with U.S. passports. Live in sunny Israel. Vote in both countries! And they say they can love America and Israel at the same time. But lately, the relationship resides under a new strain.

Every U.S. politician who speaks in Israel delivers sweet words about shared values and unprecedented alliance, not to mention $3 billion in annual U.S. aid between the best-friend nations. It’s a bond so close that many in both nations envision Israel as “the 51st state.”

But today, the talk here around American Israeli dinner tables is all about the open feud between President Obama and Prime Minister Benjamin Netanyahu, about who disrespected whom, in a sensational public spat over the pending deal to curtail Iran’s nuclear ambitions and whether Netanyahu meant it when he said there would never be a Palestinian state under his watch.

As marriage counselors say, in many rocky relationships, the problems on the surface may run much deeper. The U.S.-Israel relationship is now increasingly viewed here by ordinary citizens along Washington-style partisan lines.

Few feel this more intensely than these dual citizens, who might choose between Fox and CNN on their satellite TV packages.

The U.S. and Israeli flags fly on the roof of the Agripas Boutique Hotel in Jerusalem. (David Vaaknin/For The Washington Post)

On the right, many American Israelis blame Obama. They say he doesn’t understand Israel’s deep anxieties, or worse, doesn’t really care.

“He has written off Israel,” a popular Israeli columnist wrote. Some disparage the U.S. president, placing emphasis on his middle name, Hussein. They recycle old tropes that he is a stealth Muslim or is against Jews.

On the left, American Israelis say Netanyahu is the problem. He’s a bully, an embarrassment, he’s turning the whole world against us; he insults America, Israel’s only true friend, they say. They point out, with exasperation, that most American Jews are Democrats who voted for Obama.

Pundits call Netanyahu the de facto president of the Israel chapter of Republicans Abroad. His critics call him a bot for billionaire Las Vegas casino owner, Jewish philanthropist and super-GOP donor Sheldon Adelson. Adelson owns the largest circulation newspaper in Israel, often a house organ for Netanyahu and his Likud party.

Yet even among committed Democrats in the American Israeli community, there is a thrum that the Obama White House may not get it — that either the president has failed to communicate why the Iran deal is good for Israel or has been outfoxed by Netanyahu, who was reelected last month for a historic fourth term.

There are no official figures for the exact number of American Israelis in Israel, in part because the population is so mobile. It includes Jews, Muslims and children born to expatriates living here. A widely accepted estimate is 200,000 or more.

Some live in Israel for deeply religious reasons; others are secular Zionists. There are ultra-Orthodox communities in Israel and the West Bank that are filled with American Jews who largely eschew foreign policy discussions. There are also American transplants in Tel Aviv who live on Twitter and offer dozens of opinions on U.S.-Israel relations every day.

Debra Pell, an American Israeli who lost relatives in the Holocaust, says she remains “very much American . . . with two loves” but frets over Israel’s direction (David Vaaknin/For The Washington Post)

“I am a bridge person. I am still very much American and live with two loves,” said Debra Pell, 59, a venture capitalist in Jerusalem, whose grandparents were killed in the Holocaust.

“My children speak English with me and Hebrew with their dad,” she said. “I go back to America three or four times a year. I leave with one suitcase and come back with seven.”

Pell said the breakdown between Netanyahu and Obama is more than “a personality clash. It is much deeper.”

She worries that Israel no longer shares values with the United States, that Israel is a new democracy but growing harder, more insular and less democratic. “There were clearly some racist views coming from the prime minister,” she said, when Netanyahu on election day warned that Arab Israelis were voting “in droves.”

“I have my own serious reservations about the Iranian agreement, but the way that Netanyahu went about criticizing the agreement is lethal for U.S.-Israel relations,” she said.

Yona Sprecher doesn’t like the Iran deal, and he doesn’t like Obama. The New Yorker immigrated to Israel 15 years ago and works as a property manager for Americans who own apartments and villas in Israel.

“There is a wide range of Jews who are very afraid of what will happen in America and Israel because of this deal with Iran,” he said. “They believe it will be dangerous.”

Sprecher, 40, lives in the city of Beit Shemesh, between Tel Aviv and Jerusalem, and identifies himself as a modern Orthodox Jew. He said the bad blood between Israel and the United States was created by Obama, not Netanyahu. “I think it is one man, a very evil man, who has caused this to happen,” he said.

American Israelis may live, work and study in both countries. They send their children to American universities and to Jerusalem yeshivas; they do business in New York and Tel Aviv. Many have family back home.

Unlike many immigrant communities across the world, the American Israelis do not adhere to a single Israeli party or political persuasion.

Many come over as young adults and are just beginning their lives as Israelis.

Shayna Abramson Kovler, a graduate student of political science at Hebrew University of Jerusalem, arrived two years ago.

“I think I could live here for 20 years and will always be a New Yorker,” she said. “I think in some ways I feel Israeli, but I think that acculturating into Israeli society is a lifelong process.”

Kovler voted for Obama. “I feel a little disappointed, because I think he is letting his personal feeling for Netanyahu affect his policy for Israel,” she said. “I do not think that this is anti-Semitic or anti-Israel.”

Dorit Raviv said she had a “real American life growing up in Los Angeles” with a swimming pool and a recreational vehicle. She immigrated to Israel 17 years ago but still hits Costco when she goes back to the States.

“I have never bought a deodorant in Israel. I have the brand I like from there,” she said.

Raviv, 39, who works in the education department at the Yad Vashem Holocaust remembrance museum in Jerusalem, supported Netanyahu’s decision to address a joint meeting of Congress and to oppose the Iran deal. She believes Netanyahu was correct to say the time was not right for negotiations with the Palestinians.

“I was very upset with the things that Obama said. I don’t think he really understands the real meaning of Israel,” she said. “He does not understand why we can’t have peace here; he can’t see that we are living amongst people who hate us.”

After Netanyahu said he would oppose a Palestinian state as prime minister, Obama said Washington would “reassess” U.S.-Israeli relations.

“I am not worried,” Raviv said. “I guess as an American citizen, I can always go back, or I can stay here and suck it up.”

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