The beach closings that you have been hearing about affect only those stretches of the Cape Hatteras National Seashore that are not adjacent to the towns of Hatteras Island. So let me be very clear:
The beaches from the 4 wheel drive areas of Carova, etc. down to Nags Head are unaffected and open.
The beaches adjacent to Rodanthe, Waves, Salvo, Avon, Buxton, Frisco, and Hatteras are unaffected. You can still walk onto the beaches just like you always have.
What may be affected are the ramps leading onto the beaches that are not directly adjacent to the towns on Hatteras. As an example, there are 15 miles of beach between Salvo and Avon. There are beach access ramps allowing people to drive onto the beach throughout this stretch. If you want to drive onto this part of the Cape Hatteras National Seashore (versus just walking from your house onto the beach in whatever town you are staying), you may find these ramps closed. The greatest affect comes to those who like to drive these largely uninhabited stretches to go fishing or swimming. That is where the Park Service may close the beach. The uproar has to do with closing these stretches because many people enjoy driving to and fishing/swimming, and so forth along these stretches.
NOTE: The yellow indicates that only foot track is allowed on this stretch of beach (no vehicles). Largely this is by the towns of Hatteras Island (Rodanthe, Waves, Salvo, Avon, Buxton, Frisco, Hatteras), but these stretches have always been for pedestrians only to protect teh people from these towns from being hit by a four wheel drive vehicle. It is the red stretches that you need to watch for and only if you are planning on spending your time someplace other than the beaches of the towns of Hatteras Island. Your vacation will be largely unaffected.