So here’s the situation on the National Mall:
The Smithsonian museums are closed, but construction continues on the National Museum of American History’s Public Space Renewal Project . . .
. . . and the National Museum of African-American Culture and History:
The World War Two Memorial is open to the Honor Flight groups, but access is limited to one entrance on one side with the rest closed off:
Apparently the District of Columbia War Memorial, not far away, isn’t important enough to close. It has no barriers, fences, or tape:
Across the street is the Martin Luther King Memorial, which is, in fact, closed . . . but while I was there, there were no National Park Service personnel to prevent people from entering. So some people just jumped the fence.
Moving along, the Korean War Memorial, technically closed, had the most visitors . . .
. . . although the Vietnam Veterans Memorial came close:
The fence blocking off the Vietnam Veterans Memorial had been moved, and the visitors ignored it:
But no one dared jump the fence at the Lincoln Memorial.
In short, the National Park Service has technically closed all of the monuments, but the level of enforcement varies widely. Perhaps their staff recognizes the public relations fallout that would result from arresting tourists for trespassing.
Finally, all of the visitors to the World War Two Memorial walked by this engraving: