It's fun to poke fun at the Federal government on Internet forums. It's fun to talk about our rights. It's fun to theorize what law will hold and what won't. But none of us are lawyers. It is quite another matter altogether to drive hundreds of miles to see "park closed" sign. It is quite another to be told to go home, go in anyway, get detained, held, charged, and having have to show up in court - even if you are ultimately cleared of wrong doing.
I would suggest OP to call the park services and find out for sure. If you decide to disobey on moral grounds, better carry a phone number to your lawyer.