The Christian Science Monitor reports, here:
Under a 1981 memo by then-budget Director David Stockman, which is still in effect, the federal government in shutdown mode is allowed to keep policing and protecting “federal lands, buildings, waterways, equipment and other property owned by the United States.” Other essential services cannot be funded, however, including most of the primary mission of the Park Service: providing guidance and interpretation for visitors.
In that way, visitors coming into the parks could be seen as a distraction for rangers providing basic protection, land policy experts suggest.