Whether parks would remain open during a government shutdown next week remains to be seen/NPS file

Though federal agencies were being told Thursday to prepare for a shutdown if Congress fails to reach a budget agreement before October 1, whether national parks would stay open for visitors remains to be seen.

Under President Trump parks remained open during the budget deadlock in 2018-19, though services were shuttered and park personnel reduced. 

Thursday's notification to federal agencies to prepare for a shutdown was procedural, and agencies were sorting out how they would operate.

National Park Service staff in Washington, D.C., couldn't say whether parks would remain open in the event of a shutdown, and pointed the Traveler to the Operations in the Absence of Appropriations | U.S. Department of the Interior (doi.gov) webpage. 

That page, which soon was taken down, had a link to a document concerning NPS operations in the event of a shutdown. Drafted by the Trump administration, the document (attached below) stated that "Parks must notify visitors that the NPS will cease providing visitor services, including restrooms, trash collection, facilities and roads maintenance (including plowing), campground reservation and check-in/check-out services, backcountry and other permits, and public information. National and regional offices and support centers will be closed and secured, except where they are needed to support excepted personnel. These steps will be diligently carried out while still ensuring visitor and employee safety as well as the integrity of park resources."

Additionally, the document stated that, "(S)taffing levels will be based on the assumption that no visitor services will be provided. While parks may still be accessible to visitors, parks may not use the presence of visitors in the park to justify higher staffing numbers than approved during previous shutdowns."