Gates should be locked.

Especially National Historic sites like Harper's Ferry, or Mt. Vernon, where there needs to be a 24/7 presence to care for animals and grounds.
Or the National Mall - which has no gates or fences to speak of; likewise, parks like Yellowstone where a highway runs through it, and which there are overnight lodges or seasonal campgrounds open during the winter where groups may have booked a week or two and got there prior to the shutdown - and may still be at the site without services.

Visitors may or may not be able to easily get into a National Park or Monument, but in a lot of cases - especially National Forests - but they can easily get to these sites using a road maintained by the state or county also used for daily/resident traffic as well as park traffic - a road that can't be locked up or closed. In most cases, someone who wants to hang out at one of these places can just hop a restraining arm that typically blocks off the parking lot or road after hours and walk in.
There won't be any services, and maybe the restrooms might not be open, but one can still spend time and get into whatever mischief they want to.

Haele

And were surprised that the Clinton Presidential Library was closed. I was under the impression that they were run by private foundations.
Of course the bar, and gift shop were still open (in case Bubba wanted a beer I guess) but all exhibits were closed.

There is more to this shutdown than than the Department of Interior and the average poor person is NOT going to a national park "for vacation".

They need to talk more about the diminished capacity of those who are inspecting and testing your food and water, inspecting the nuke facilities, monitoring the weather, monitoring those Americans up in the International Space Station, those completing/approving paperwork for student loans for the upcoming college semester, those who work with states to manage Section 8 housing, those who maintain the systems that host SNAP and handle customer issues, the bureaus that deal with natural disasters or farm subsidies, those working on a myriad of investigations of train derailments or plane crashes, and even those who support the courts, which are already backlogged.

It's just mind-boggling the trivialization that the media does every time this happens.