But it gives Ms. Rutter more options as she works to shape the Kennedy Center and navigate what it means to be the National Cultural Center — as it was designated in the original legislation that created it — in Trump-era Washington.

It was perhaps unsurprising that Ms. Rutter, a respected veteran of the orchestra world, would win praise for helping turn around the underperforming National Symphony Orchestra by hiring the dynamic conductor Gianandrea Noseda as its music director. But she has also branched out, making the Kennedy Center a destination for stand-up comedy and expanding its hip-hop offerings under the aegis of Q-Tip, of A Tribe Called Quest, the center’s first artistic director of hip-hop culture.

At times the Kennedy Center feels more like a regional arts center than a national one, presenting theater tours and visiting dance companies. But it also runs Washington National Opera and the National Symphony Orchestra (whereas at Lincoln Center, the Metropolitan Opera and the New York Philharmonic are independent organizations) and produces some theater work . It is best known nationally for its televised Kennedy Center Honors; unlike past presidents, President Trump has chosen to stay away from the performances after some honorees criticized him.

Ms. Rutter said she did not believe the center’s art should be “overtly political” because it is officially a living memorial to President John F. Kennedy. (As a memorial, it gets roughly $40 million a year in federal aid to maintain its buildings and grounds; the rest of its budget, which ranges from $210 million to $230 million a year, comes from ticket sales, earned revenues and donations.)