A nude beach self-selects for people who think that public nudity is not a big deal. You are choosing to be nude around a bunch of people who probably won't care. If only they know about your nudity, no negative consequence is likely to befall you.

Outside of your time at a nude beach, you deal with all sorts of people who may think it is a big deal and judge you for that. It may be in your interest to keep such people out of the know of your time at the nude beach. Think neighbors, employers, other parents in your PTA.