The 2016 Olympic Games have been billed as an opportunity to put politics aside in the spirit of international camaraderie, but that’s not necessarily how it’s working out for Israeli athletes.

Animosity toward the 47-member delegation has triggered a reprimand from the International Olympic Committee and alarm from Jewish groups such as the Anti-Defamation League, which issued a statement this week decrying anti-Israel “hostility” in Rio de Janeiro.

“Shocking but not surprisingly, the Lebanese and Saudi delegations obviously have the wrong idea about the Olympic Games,” said a statement Wednesday by Roz Rothstein, CEO of the pro-Israel group Stand With Us.

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“Instead of using the events to forget animosity and promote peace between people, they have brought their brainwashed minds to Rio,” she said. “How unfortunate that they could not implement the good, peaceful intentions of the Olympics, and instead have used it as a forum to spread hate and continued rejection of peace.”

The confrontations with delegations of nations traditionally hostile to Israel have marred an otherwise successful Olympics for Israel. Two days ago, judo fighter Yarden Gerbi won the bronze medal, making her the nation’s first medal winner since the 2008 Olympics.

On Sunday, however, the IOC issued a reprimand to the head of the Lebanese Olympic delegation after he blocked Israeli athletes from entering a bus that the teams were supposed to share to reach the opening ceremony.

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Instead, Olympic organizers placed the Israeli athletes on a “special vehicle,” said Israeli sailing team trainer Udi Gal.

“The bus driver opened the door, but this time the head of the Lebanese delegation blocked the aisle and entrance,” Mr. Gal said on Facebook. “The organizers wanted to avoid an international and physical incident and sent us away to a different bus.”

He said he was “enraged and shocked by this event.”

“How is it possible that they let something like this happen and on the opening night of the Olympic Games?” he said.

Miri Regev, Israeli minister of culture and sports, blasted the Lebanese incident as “anti-Semitism, pure and simple, and the worst kind of racism.”

The Lebanese delegation head, Saleem al-Haj Nacoula, who was reportedly hailed in Lebanon as a hero, told Arabic media that he was “surprised to see the Israeli delegation approaching and trying to get on.”

“I told the bus driver to close the door, but a trainer who was with the Israelis prevented him from doing so,” he said, as reported by The Times of Israel. “I had to physically stand at the door and block him and the rest of the delegation from boarding, knowing that some were trying to force their way through and were looking for trouble.”

Days later, Joud Fahmy of Saudi Arabia forfeited a first-round judo match Sunday in what the Israeli press described as a tactic to avoid facing Israel’s Gili Cohen in the second round.

The Saudi team disputed the charge, insisting on Twitter that Ms. Fahmy had sustained injuries to her arms and legs during training, although episodes of Arab and Muslim athletes refusing to compete against Israelis are relatively common in international sports.

In June, Syrian boxer Ala Ghasoun refused to participate in an Olympic qualifying match against an Israeli, saying that to do so “would mean that I, as an athlete, and Syria, as a state, recognize the state of Israel.”

“I quit the competition because my rival was Israeli, and I cannot shake his hand or compete against him while he represents a Zionist regime that kills the Syrian people,” Mr. Ghasoun said in Arab media, according to Jerusalem’s i24 News.

During the 2012 London Olympics, Iranian judo champion Javad Mahjoud withdrew from a match against Israeli Arik Ze’evi. Mr. Mahjoud cited health concerns, but he previously admitted to throwing matches to avoid facing athletes from Israel, according to the Anti-Defamation League.

Israel’s national soccer team and its clubs have to compete in the World Cup and the continental tournaments in Europe rather than Asia, as geography would dictate, because so many Middle Eastern countries refuse to play them.

Israel’s critics say the Jewish state is not blameless in violating the Olympic spirit. Before the Rio Games, the Palestinian Olympic committee accused Israel of delaying deliveries of uniforms and equipment, which Israeli authorities denied.

Shortly before the Olympics, several media outlets, including the Canadian Broadcasting Corp., reported that Palestinian swimmer Mary al-Atrash was unable to train at a 50-meter Olympic-sized pool because of Israeli travel restrictions.

“There is no Olympic-sized swimming pool in the Palestinian territories that Palestinians are allowed to use, so Atrash practices at the YMCA in Beit Sahour, near Bethlehem,” the CBC said in its Aug. 1 article. “The pool is 25 meters long, half the length of the facility she’ll compete in at Rio.”

The reports drew a heated response from the Tablet’s Liel Liebovitz, who dismissed the Palestinians-have-no-pool story as a hardy perennial in Olympic years, even though he said the territories have several 50-meter pools at which Ms. al-Atrash could train.

Mr. Liebovitz also pointed to a statement in July by an Israeli agency saying the swimmer would have been welcome to train in Jerusalem if she applied for a permit, which “like Palestinian athletes before her, she refused to do.”

Fans of the Israeli team were also indignant last week after Facebook failed to post the Israeli flag on its Olympics page. After a complaint by the Olympic Committee of Israel, the flag was added.

“We experienced a short-lived technical issue that prevented the Olympic profile frames for some countries from being displayed correctly in the profile picture selection menu,” Facebook said in a Wednesday statement. “We’ve since fixed this and now all countries should show up in that list.”

While the string of incidents has left supporters of Israel indignant, none comes close to the horror of the 1972 Munich Olympics, in which 11 Israeli athletes were kidnapped and killed by Palestinian terrorists.

“These days, anti-Israel vio­lence at the Olympics has been replaced by politics,” the Anti-Defamation League said in a Monday statement, “with representatives from countries hostile to Israel going to great lengths to avoid any interaction with Israeli athletes.”