I haven't had any issues driving around the various towns (Nags Head, Carolla, Kill Devil Hills). I do usually run around with my motorcyle mirrors on when I have my doors off. There are lots of other Jeeps running around naked, so you won't be alone. If you are worried about local laws, amazon has several cheap mirror options that will keep you compliant.
If you get a chance to drive on the sand, I highly recommend it. Nags Head, KDH, etc only allow beach driving in the winter. North of Corolla can be driven any time as that is technically the road up to 4x4 beach. You will need a permit if you plan on stopping, there are also rules about where to park, see their websites. The Hatteras state park also allows driving on the sand year round, you just need a permit. And the permit is easier to get online before you go.
Each of the towns has a website explaining the rules, fees/permits, timing. Just realize each town is different, so you'll need to research the area you plan on spending time at.