Comedian Bill Cosby performs during a show last year at the Maxwell C. King Center for the Performing Arts in Melbourne, Fla. (Phelan M. Ebenhack/Associated Press)

THE SMITHSONIAN Institution has taken heat for its controversial exhibition of art from the collection of Bill and Camille Cosby. Good — officials have only themselves to blame for the missteps in mounting the exhibit and the clumsy responses to criticism. They are, though, right in refusing demands to shut down the exhibit.

As allegations of sexual abuse against Mr. Cosby have mounted, including the comedian’s disturbing testimony about his sexual behavior from a settled civil suit, other organizations have severed ties with him. NBC and Netflix dropped plans for new projects, TV Land stopped airing reruns of “The Cosby Show,” Spelman College terminated a professorship funded by the Cosby family and Disney’s Hollywood Studios theme park removed a statue of him. The National Museum of African Art, however, has stuck by an exhibition, “Conversations: African and African American Artworks in Dialogue,” which intersperses pieces from the Cosby family’s well-regarded private collection with those of the museum.

It opened in November, just as rape allegations against Mr. Cosby began to publicly percolate. Johnnetta B. Cole, director of the museum, said in an explanation posted this month on the Root that she was unaware of the allegations. “Had I known,” she wrote, “I would not have moved forward with this particular exhibition.” No question there are unfortunate, even embarrassing, aspects of the exhibit — the quote from Mr. Cosby emblazoned on the wall about quilts telling a story “of life, of memory, of family relationships” comes to mind — but Ms. Cole is correct that the exhibit comes down to the artists, their work and the ability of the public to appreciate both.

It is a generally accepted standard that museums don’t change exhibits once they are in place lest they be seen as succumbing to censorship or political pressure. A vivid example of the Smithsonian falling into that trap occurred when former Smithsonian secretary G. Wayne Clough bowed to political pressure in 2010 and yanked a video from a National Portrait Gallery exhibit exploring gay themes in art history. Pulling or changing “Conversations” before the end of its scheduled run in January would echo that mistake and would harm artists who bear no responsibility for Mr. Cosby’s actions.

We are glad, though, that the museum last month finally posted a sign outside the exhibit saying it doesn’t condone Mr. Cosby’s behavior. Clearly, officials should have moved sooner to address Mr. Cosby’s appalling actions as well as concerns about conflicts of interest and transparency that have arisen. Camille Cosby sits on the museum’s advisory board, and the family donated $716,000 to help with the cost of the exhibit. Giving public display to private collections can increase their value and so must always be undertaken with care. That’s particularly critical when the display occurs on the Mall, so let’s hope the Smithsonian has, at least, learned some lessons from this painful experience.