This is a really tough one to answer. It depends entirely on how open-minded your parents are. Try to instigate some philosophical discussions about nudity and how you feel about it.
Here's an example, but by no means am I trying to put words in your mouth.
You: Did you hear about that guy who got arrested for changing his clothes on the tennis court?
Mom: Yea. Why would somebody do something like that?
You: Don't you think it's ridiculous that people seem to think that nudity is so offensive that people have to be arrested because somebody saw their nude body? I'm not talking about flashers or anything like that. Just people being people. What's wrong with the way we were born? Why are certain body parts percieved as offensive? I mean, just because somebody is nude doesn't mean that they have sex on their mind.
Here's where your mom will either freak out and wash your mouth out with soap, or she'll see your point of view.
Now that your folks know how you feel about nudity, it'll be a lot easier to let them in on your desire to be a nudist. Of course if they freak out, you may want to keep your nudist tendencies to yourself until you're older. After all, you've still got to live with them for a long time. Just use your better judgement.
I have enclosed a couple of links for family friendly and clothing optional resorts in Georgia, in the event of you being able to convince your parents to take you there for a weekend. (They can keep their clothes on....lol )
I hope I've been of some help.
Sharon