(My apologies, it's a bit late for coherent writing, but I wanted to finish this before time gets away from me.)
So, back to modesty. What is it really all about? I think it's about avoiding pride. If we look at it this way, the admonition to be be modest in our dress has more to do with dressing so as not to intentionally draw undue attention to ourselves, being "free from conceit or vanity." Wearing a swimsuit to church would be immodest, because it would serve to draw attention to myself. Going swimming in tuxedo would likely have the same result. It seems that it is all about our attitude in the clothing choices we make. The outcome we desire has an impact on the correctness of an action.
If our attitude is what determines our level of modesty, I have a hard time seeing a problem with going naked at a nude beach. Assuming one's desire is not to have others be impressed by one's physique, the situation seems analogous. The nudity would not attract any undue attention, because others would be nude, and expecting to see nudity.
What this implies is that there is nothing wrong with nudity per se. It can be non-sexual. That is not to say that any nudity is modest. Certainly, the contrast is easily seen with a strip club. There, regardless of how much skin is currently being shown, the revealing nature of the clothing worn is designed specifically to gain attention (what's more, in a sexual way). This is most obviously immodest. But it doesn't seem to be the nudity itself that is immodest, but rather the intent of the stripper, the way she behaves in attempting to draw attention to herself.
Now, anyone who wants to say there's no such thing as non-sexual nudity has forgotten what it is like to be a kid. I don't know how many times I've seen my nephew bolt from the bathroom, leaving a towel lying somewhere in his path, and running around the house naked. Why? Because he doesn't enjoy clothing. They bother him. He hates shoes. Pulls his socks off constantly. And if you leave him alone long enough, he'll remove everything his little hands are able to.
For me, I've worked in a health care setting for a few years. I've seen naked body after naked body, and I can tell you that the amount of sexual tension in that encounter is entirely dependent on me. If I have it in my head that nudity is sexual per se, then every time I see a patient that's going to be an issue. But if I get used to the idea that nudity is simply... nothing. It's not anything. It's a lack of something. It's like zero, not even a real number (I'm not talking about actual sets of numbers), it's the absence of numbers. It's "clothlessness." For me, at work, a body is simply, a body. A diagnostic tool. A source of information. And, more importantly, a person... just without all the trappings.
For me, I seem to have become a "nudist" without ever really thinking of myself as such, or participating in a nudist lifestyle. I don't think there's anything wrong with the naked body. When I go to work and see nudity, it doesn't ever cross my mind that it's sexual in any way... because it's not. (To be honest, the first few times it happened, it was at least a little sexual for me. But that was due to my incorrect perception that nudity and sexuality always go together. It's no longer an issue... really) When I get done exercising, and shower at the gym, I see lots of other guys nude... but it is again not even remotely sexual. When I give my nephew a bath, I see him nude. But guess what... still not sexual.
Some of the most beautiful art ever created was of the naked form... seeing David in person was breathtaking for me. I think we need to remember that art is an imitation. As great as Michelangelo was, he cannot compete with the beauty that God has created in us, in giving us our bodies. I think it is tragic the way we have linked all nudity to sexuality, teaching even small children that there is something dirty about their bodies, such that they must be covered. They are beatiful creations. God said they were good. Who are we to argue with that, or to say that they need decoration to look appropriate?
(I'm tired, so I'll just briefly mention this, since it is likely to come up for some people: I think it is flat wrong to teach the young women of the church that it is their responsibility to control the thoughts of the young men, by dressing in a way that would not be sexually appealing to them. It tells the girls that if they do get inappropriate attention, ogled, harassed, or raped, that somehow it is their fault. And IT'S NOT! If I can be expected to not look at patients in a sexual way, there is no reason that all men (young or not) shouldn't have the same expectation in daily life.)
If I can do it at the office (as in, not equate nudity with sexuality), why not at the beach? Or a pool? Hot tub? Party?? Home?
For the interest of full disclosure, I'm not sure how I feel about the whole social nudity idea in relation to Mormonism, but I am having trouble finding good scriptural reasons for its proscription.