While the usual crowds swarmed Muir Woods and Alcatraz Saturday, visitors to many of California’s most popular national park sites began to experience the inconvenience that comes with fewer rangers, locked restrooms and shuttered information centers.

As the initial impacts of the federal government shutdown took hold Saturday, National Park Service officials strove to keep open as many attractions as their freshly trimmed budgets allowed.

Park visitors were able to access most public lands, even benefiting from waived entrance fees at Yosemite, which invited people in while closing its entrance stations and sending home the rangers who collect the tolls. But visitor services were curtailed at parks nationwide, which sometimes came with a different price.

“She wanted to use the bathroom,” said San Jose resident Nes Ab, 29, who was visiting Muir Beach with his friend Krista Katzenmeyer, 24, and found the parking lot closed and the restrooms locked. “I didn’t expect this.”

Katzenmeyer added, “If you’re going to shut down the government, at least leave the gates open.”

Like national parks across the country, the Golden Gate National Recreation Area, which manages Muir Beach as well as Muir Woods, Alcatraz and other Bay Area properties, was taking a patchwork approach to operations, keeping some areas open and closing others.

Park officials declined to discuss their plan, but said the lack of employees working because of the shutdown would force them to shutter more areas Sunday, including Muir Woods, Stinson Beach, Fort Point and Fort Funston.

“We came to California just to see the redwoods,” said Skaneateles, N.Y., resident Gary Prochna, 61, who was visiting the towering old-growth trees of Muir Woods on Saturday morning with his son Ryan, 23, and was glad to get in before it was closed. “They’re beautiful.”

Alcatraz Island was scheduled to remain open because it’s operated largely by a private company. So were most spots in the Presidio, which is run by the independent Presidio Trust.

But while additional parking lots and restrooms within the Golden Gate National Recreation Area were expected to close Sunday, that’s not likely to stop visitors from finding alternative parking and sidestepping entrance gates into the sprawling park, which covers 82,000 acres.

Saturday’s service interruptions are the second that the National Park Service has endured this decade. Government services considered nonessential were similarly shut down in October 2013, though park leaders took a different approach then: They closed everything as quickly as they could.

This time around, however, Interior Secretary Ryan Zinke instructed parks to remain as accessible as possible while still ensuring the protection of public lands and the safety of visitors.

Interior Department officials couldn’t be reached for comment Saturday, but the National Parks Conservation Association estimated that more than three-quarters of the park service’s 20,000-plus employees were being furloughed.

Most parks were choosing to keep law-enforcement rangers and emergency responders on the job, but maintenance staff, interpretive guides and researchers were being sent home until normal funding resumes.

At Yosemite, between 100 and 200 of the park’s nearly 800 government employees were sticking around, said park spokesman Scott Gediman. The staffing reduction meant visitors were basically on their own.

“If you break your leg or something happens, we’ll be there, but our response (time) will be lengthened,” Gediman said.

Visitor centers, campgrounds and restrooms were closed throughout Yosemite. The park’s independently operated businesses, however, remained open, including the Majestic Yosemite Hotel — formerly the Ahwahnee — and the Yosemite Lodge at the Falls, as well as the valley’s various restaurants, gift shops and stores.

The situation was similar at other national parks, with government services scaled back but with concessions continuing to operate at Sequoia-Kings Canyon, Joshua Tree and Death Valley.

Theresa Pierno, president of the National Parks Conservation Association, said it is only a matter of time before the parks suffer from the limited staffing. If the trash isn’t being picked up and the restrooms are closed, she said, permanent damage could be done to natural and historical resources.

“It’s not a tenable situation,” she said. “The reality is most of these national parks are going to have to be partially closed or they may have to shut down completely.”

Nationwide, many park sites started denying entry Saturday, including such iconic spots as New York’s Statue of Liberty, Philadelphia’s Liberty Bell and Martin Luther King Jr.’s childhood home in Atlanta.

Kurtis Alexander is a San Francisco Chronicle staff writer. Email: kalexander@sfchronicle.com Twitter: @kurtisalexander

What’s closed

To see a list of closed sites in the Golden Gate National Recreational Area: http://bit.ly/2DSThSb