I think that what @bright_eyes00 just said hints at the underlying reason of why people are nervous about nudity. There are only certain things that we try to protect our children from, and one of the major ones is sexuality, and knowledge of sex. Since nudity, if done properly (;-), exposes sex organs, it is associated with sex, and we don’t want our kids exposed to sex. It’s embarrassing. “What’s that, Mommy? Why does that guy have such a hairy peepee?” Or, god forbid, “Why is that man’s peepee sticking up?”
Or, perhaps men and women are afraid they will see nude bodies, and they will get so aroused, they won’t know what to do. Everyone will be secretly masturbating under their beach blankets. Men won’t know how to keep from getting an erection.
I haven’t been at all that many nude beaches or places where nudity is common (maybe 3 or 4), but I’ve never seen a problem like this. It’s just bodies and no one makes a big deal of it. Most people are just sunning themselves, or swimming. Or they are in the baths together. Japan, for ages, had common public baths and the custom was to be unclothed in them. This may have changed in the last few decades, but perhaps it is still the custom.
The taboos about nudity are purely cultural. There is no objective reason for them. Americans are hungup about sex, so they think nudity is a big deal. Nudity = sex. Other cultures don’t make the same connection. So it’s no big deal, and parents don’t feel a need to protect children from it.
This question asks a normative question. There is no objective answer. It all depends on your personal taste, which is based on the culture you grew up in, or on your philosophical or political or religious ideas. If you think nudity is inextricably linked with sex, and if you think children shouldn’t know about sex, then it isn’t ok to take your children to a nudist beach. If you think nudity is just bodies, and isn’t related to sexual thoughts, or if you have no problem with your kids understanding what sex is, then you won’t have a problem taking your kids to a nudist beach.