The reasoning is that if you allow clothed people on the beach, you'll get more and more clothed people until naturists are a minority and don't feel comfortable getting naked. And because naturists don't have a lot of places to practice it, they are quite protective of the few places they do have.

Yes it's bad. If people begin wearing clothes at a nude beach, it won't be a nude beach for very long.

I don't know. I would just assume if you're clothed, you don't really need to be on a nude beach, and I'm sure there are enough pervs sitting around watching.

There's really no reason to be on a nude beach unless you're going to participate. Usually there's a clothed beach right next to it.

Where

Where do they put the badge?

That's what's known as an MPI (Mandatory Penis Inspection)