In DC in the last year we had a vandal deface the Lincoln Memorial and the National Cathedral. If during the shutdown the National Park Service just left all of the monuments unguarded and someone took a hammer to the nose of a statue of Jefferson, that'd be a humongous price to pay. In a national park, without park rangers to rescue people, if someone got themselves into trouble and died, that would be worse than ruining some people's vacations.
It is possible that the White House ordered parks and monuments closed for political reasons, but that's all speculation at this point. No different than speculating that George W. Bush allowed 9/11 to happen to justify invading Iraq.