Not everything "in public" is a statement made with the consent to be recorded, shared over the internet by bystanders, exploited by corporations and archived for eternity. A public nude beach, and take note that this thread is actually about a private nude beach but let's argue the weaker point, is a place for people to be nude, not a place to be exploited to make porn. The fact that it is physically possibly to exploit a nude beach for softcore porn does not mean it is acceptable. In the same way that being nude at a shopping mall is physically possible, but socially not acceptable and mostly also not legal. Please note that nudism and exhibitionism are not the same.

For most participants Nudism is about freedom of self and a return to nature, it is about oneself, not about society or making statements, and not about pushing ones own nudity into other peoples faces. That would be exhibitionism. Many nudists are quite shy and not interested in becoming someone else wank material, or an actor on national television, or instahub. They do not wish to be recorded. They just want to be nude at the beach, there is no larger meaning or implied consent. Let me repeat that: being nude at a nude beach does not automatically imply consent to be filmed by anyone for any purpose. And we can argue this finer detail of "privacy" as being different from "privatly/publicly" and how it hinges on consent, without looking at nudism in particular:

Imagine every time you leave the house a national television crew follows you around. It doesn't actually matter what you do, they will cut and manipulate the footage to fit their narrative. You are not getting paid and are not consenting, and you have no influence on what the show is about. But it is going to be degrading, let's call it "americans most stupid". You should have stayed inside if you don't want to be exploited like that. This is the american idea of privacy: once you step outside, you have none. The usa does not differentiate between "being seen on the street, at a bar, at a beach" and "being published on national television, on instagram, on pornhub". If you want to use the former, you must accept to be exploited by the later and their endless supply of unpaid content creators. The european interpretation says that these people are not content creators, but creeps that are violating your human right to privacy and self determination by recording and publishing your activities without your consent.

The public is facing the tragedy of the commons as "public spaces" have become freely and easily exploitable by corporations in the age of surveillance capitalism and social media.

Note that european style privacy law is differentiated in the finer details: a person who films at a nude beach can claim to do so as a technological extension of their own personal memories and with no intention to publish the material and that is not in violation of privacy laws. This is the case in the thread starter. For the law it is the exploitation of the material, turning personal data of unwilling subjects into commodities without their consent, which is illegal. This is a detail most people at nude beaches do not like: they find the act of filming itself to be as creepy as a wanker sitting in the bushes.