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.