The top official overseeing theater at the John F. Kennedy Center for the Performing Arts is stepping down, throwing into question the stability of one of the venue’s most important sources of box office revenue as President Trump seeks to transform the institution.

Jeffrey Finn, whose current titles are senior vice president of artistic programming as well as vice president and executive producer of theater, plays an outsize role at the Kennedy Center. For nearly a decade he has programmed its touring Broadway shows and locally produced musicals, which have often sold strongly.

While theater has been a financial driver for the Kennedy Center, the future health of the theater program has been called into question as some Broadway producers and performers have said they were uncomfortable working there as Mr. Trump seeks to put his ideological stamp on it. During Mr. Finn’s tenure he booked two successful runs of the musical “Hamilton” there, but the show’s producers canceled a planned third run because of Mr. Trump’s actions.

Mr. Finn declined to comment, and Kennedy Center officials did not respond to requests for comment. Mr. Finn’s resignation was confirmed by two people with knowledge of the move who asked not to be identified because they had not been authorized to speak about the matter by the Kennedy Center.

His resignation comes at a time of change for the Kennedy Center. Mr. Trump, early in his second term, purged board members appointed by former President Joseph R. Biden Jr. from the previously bipartisan board and had himself appointed board chairman. Last month, Republican lawmakers suggested renaming the Kennedy Center’s Opera House after the first lady, Melania Trump.

And just this week Mr. Trump announced a plan to host the next Kennedy Center Honors ceremony, celebrating artists approved by him. (In: Michael Crawford, Broadway’s first, and Tony-winning, Phantom of the Opera. Out: “wokesters.”)