Visitors take photos at MOMA; image Brian Kelly

For some time, art museums have been expending considerable amounts of energy and other resources on a broad campaign of public engagement designed to establish a stronger bond between themselves and the public, and thus cement the museum’s place as an essential—even indispensable—component of public life. Social media promotes their programs and addresses the public in other ways, “crowdsourcing” guides them in their acquisition and exhibition decisions, and “crowdfunding” helps pay for them. All manner of events and programs are put on in hopes of making the museum an appealing, even hip destination. Last year, one institution—the Sterling and...