The president’s executive order demanding change at the institution presents a perilous test for Lonnie G. Bunch III, its secretary, whom the White House calls a partisan Democrat.

Because the Smithsonian can receive private funding, it is not entirely in trouble-but the long-term effects remain unclear.

President Donald Trump has signed an executive order on the Smithsonian Institution that targets funding to programs that contain what he calls “divisive narratives” and “improper ideology.”