It depends on your Airstream. There are very specific requirements that your camper and your truck/SUV must meet before you can acquire a permit to camp on the beach. That list of requirements is here: https://www.nps.gov/caco/planyourvisit/orv-equipment-and-tire-requirements.htm (and they do look very closely at your tires, etc. before issuing a permit). If you meet the requirements, I don't see why you couldn't get to the beach spots in an Airstream.