What is the impact of a federal shutdown?

National parks staff would be furloughed, but the parks themselves would remain open.

According to Reuters, a partial list of programs most likely to be affected includes:

WIC suspended: Nutrition benefits provided to 7 million mothers through the Women, Infants and Children program would be cut within days, according to Agriculture Secretary Tom Vilsack.

SNAP has just one month: Food aid through the Supplemental Nutrition Assistance Program (SNAP) would go out as normal for October, but could be affected after that.

Emergency shelter assistance: Local governments would not get new aid to shelter migrants.
School IT support: The Cybersecurity and Infrastructure Security Agency would suspend security reviews that help schools, local governments and other institutions defend against ransomware.

Washington DC: Lawmakers would continue to collect paychecks, even as other federal workers do not. Staffers would not get paid, though those deemed essential would be required to work.

Airports: Training for 1,000 new air-traffic controllers would stop, leaving the system understaffed. The Transportation Security Administration would not be able to hire new airport security screeners ahead of the busy holiday travel season.

NASA: The National Aeronautics and Space Administration (NASA) would continue to support the International Space Station and track satellites, but 17,000 of its 18,300 employees would be furloughed.
Public Health: The National Institutes of Health would furlough most of its staff and delay new clinical trials for medical treatments.

Nuclear and hazardous waste and water monitoring: Most inspections of hazardous waste sites and drinking water and chemical facilities would stop.

Food: Food-safety inspections by the Food and Drug Administration (FDA) could be delayed.

Wall Street: The Securities and Exchange Commission (SEC) would furlough roughly 90% of its 4,600 employees and suspend most activities, leaving only a skeleton staff to respond to emergencies. And the Commodity Futures Trading Commission (CFTC) would furlough almost all of its employees and cease most oversight activity.

IRS: The Internal Revenue Service (IRS) would stop examining and auditing tax returns and responding to taxpayer queries. Automated tax collection would continue, as would processing of green-energy tax credits under the Inflation Reduction Act. Roughly two-thirds of the agency’s 90,000 employees would be furloughed.