As President Obama hosted his final Hanukkah celebration at the White House on Wednesday, an umbrella organization of major Jewish groups was co-hosting another Hanukkah party less than a mile away — at the Trump International Hotel.

The dueling celebrations, the latest instance of the awkward denouement of the Obama presidency and the advent of Donald J. Trump administration, illustrated a broader rift in the Jewish community.

Several centrist and liberal organizations refused to attend the Trump hotel event, co-hosted by the umbrella group, the Conference of Presidents of Major American Jewish Organizations, and the Embassy of Azerbaijan, and over 250 people protested in the streets outside the hotel.

Protesters and groups that declined to attend spoke of Mr. Trump’s divisive statements that many say have spurred anti-Semitism and hostility toward minorities, and Azerbaijan’s human rights record.

Ori Nir, the communications director at Americans for Peace Now, a group that declined an invitation to the event, said he and his colleagues initially thought the invitation was a hoax. The group wrote a letter to the Conference of Presidents expressing its concerns. “As members of the conference we try to be discreet,” he said. “But this time around it was so insensitive that it really merited a public expression.”

Although 71 percent of the Jewish community voted for Hillary Clinton, the Jewish response to Mr. Trump’s election has been anything but unified. Some Jewish organizations issued messages of congratulations to the president-elect, while others have openly and strongly condemned Mr. Trump and his appointment of Stephen K. Bannon as chief strategist.

The Conference of Presidents includes a broad range of groups with diverse political views, like the Zionist Organization of America and HIAS, a Jewish organization for refugees. While many organizations attended the event, others issued strong statements condemning the choice of venue and the partnership with the Embassy of Azerbaijan.

The Union for Reform Judaism, the Central Conference of American Rabbis, Jewish Women International, HIAS, the Anti-Defamation League and the Workmen’s Circle were among the groups that declined to attend the event at the Trump hotel.

“To say I was surprised would be an understatement,” Ann Toback of the Workmen’s Circle, a progressive Jewish organization, said of her reaction upon learning the location and the co-host of the party. “I was horrified. It made no sense to me, and it set off a lot of alarm bells.”

The Workmen’s Circle wrote a letter to Malcolm I. Hoenlein, the executive vice chairman of the Conference of Presidents. “As a Jewish organization, we cannot and will not condone ― by agreement or silence ― the conference’s appalling choices in its partner and the location, both of which contradict the stated themes of religious freedom and diversity,” the statement read. “Everything about this event is the wrong choice.”

Mr. Hoenlein and the Conference of Presidents released a statement without further comment: “In a spirit of celebration, mutual respect and gratitude, we brought together a full house of guests from many different faiths, cultures and countries who joined together with us to reaffirm our common humanity.”

The current and former White House liaisons to the Jewish community were invited to attend the Hanukkah party as honorees, but they declined, the Israeli newspaper Haaretz reported.

Nearly 200 people, including dignitaries from Russia, the Palestine Liberation Organization and Turkey, among others, attended the party, the co-hosts said.

Josh Katzen, the executive chairman of the Committee for Accuracy in Middle East Reporting in America, attended the event and described it as “very elegant, very nice.” The controversy was not palpable, he said. “The naysayers and complainers were completely ignored and not visible.”

Morton A. Klein, the national president of the Zionist Organization of America, said he found it “incomprehensible” that organizations would not attend the event.

“I find it astonishing that these groups care more about their left-wing political beliefs as opposed to caring about developing a good relationship with the incoming president of the United States of America,” Mr. Klein said.

Allen Fagin, executive vice president of the Orthodox Union, attended Wednesday’s party and said in a statement, “We believe that the fundamentally important issue is to focus on the nature and purpose of this event and not its venue.”

IfNotNow, a social-action group formed during the 2014 war in Gaza, organized the protest outside the hotel. Organizers say interest in the group has ballooned in the weeks since Mr. Trump’s election.

Mr. Trump’s appointment of Mr. Bannon as chief strategist was the tipping point, said Yonah Lieberman, a founding member of IfNotNow. Since Mr. Bannon’s appointment, more than 3,000 people joined protests across the United States organized by the group, he said.

Other left-leaning Jewish organizations have also experienced substantial increases in volunteers and donations since the election.

“Early indications are that people are using their pocketbooks in accordance to their values,” said Rabbi Jill Jacobs, the executive director of T’ruah, a rabbinical human rights organization.

T’ruah’s donations grew thirtyfold in November of this year compared with November 2015. Rabbi Jacobs said she was heartened to see various organizations taking bold stances after Mr. Trump’s election.

“We’re seeing that organizations that haven’t spoken out this strongly before are speaking out, and I think and hope that’s the start of a trend.”

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