I'd like provide some ideas for how a teen might approach their parents about naturism. These basic guidelines can be applied to any other topic of discussion as well. How well any of these things work will depend entirely upon what sort of parents you have. Some will be more receptive to you having independent thought than others.
1. Discuss things with your parents from the position of humility.
Always remember that your parents were the ones who changed your diapers. They saw you naked right from the very start. Your nakedness is nothing new to them.
However, this also means that from their perspective you will always be their little child - even when you turn 30 or so. (Yeah, life is tough.) Often parents will have trouble letting go and allowing you to start having independent thought. Ideally there should be a shift in thinking that occurs when you turn Bar Mitzvah age (your 13th birthday or so). As you become a teen, ideally they will become your guide and your mentor to help you learn to become a mature adult and to make mature decisions. Remember that they are the teacher and you are the student. Use that position to your best advantage and be willing to learn as best you can.
Remember, that as long as you come to them with the appearance of humility and submissiveness, it will be difficult for them to be angry with you.
2. Never argue with your parents.
This will be difficult because, down deep inside yourself, you think that you are correct and that they are wrong. While this is always a possibility, remember that they have already walked the same path that you are on. They know the mistakes that they made at your age.
A helpful technique if you find that voices are starting to raise is to make your voice soft and meek. If you yell back a them, then they will only get louder and the problem will escalate. If they are yelling and are asking you a question, answer softly, with humility. When you answer softly, they have to stop yelling in order to hear you. You can actually learn to stop them from yelling at you by learning to use this technique effectively. Remember, "A soft answer turns away anger" (Proverbs 15:1)
If you see that they are reacting in anger, lower your head and attempt to withdraw from the conflict as best you can.
3. Always act a bit confused and ask questions.
Even if you think that you have all the right answers and want to show your parents what you know - DON'T! Play like you don't know a thing, rather ask your parents questions. Using keywords such as "help me". Your parents are programmed to want to help you! So instead of asking a childish "why?" style of question, formulate a question that will make them want to explain.
A properly formed question can cause your parents to start questioning their own preconceived notions about the topic at hand.
4. Study!
Always remember to study the topic at hand before asking your parents questions about it. You will then know in advance what sorts of answers they are going to give, and you can compare their answers to what you have learned on your own.
5. Think through in advance what they will give as an answer.
Ideally, as you study the topic you are going to question your parents about, you should start writing down what your question will be. Then try to come up with possible answers that they will give you in response. You know your parents, and you know the type of answers that they are likely to give. Write down each of those possible answers that you come up with. Then formulate possible follow-up questions that you can ask in response.
Again, as you ask the follow-up questions try your best to act confused. No good parent wants their child to be confused. So always try to ask for clarification because you are having trouble understanding what they are getting at.
6. Give thanks!
When they have finished giving you their answers to your questions, be very polite and say, "thank you for taking the time to help me think this issue through. You have given me more to think about on this issue."
Then, when you are dismissed, go back to the notes on the topic that you are writing and record their answers as best you can. Study more and come up with some good follow-up questions. Don't rush back the next night. Let it wait several days. Think of possible areas where their answers are not logical.
If your parents are Bible Believers, don't be afraid to ask them to give evidence from Scripture for their position. Honor your parents! But they need to help you to come to maturity in your belief as well. Looking for Scriptural support will help ground both of you in your Faith.