That's a tough one - I was diagnosed in 1966 and my parents basically gave me the same amount of freedom as my non diabetic brother and sister. I was never home, usually on a bicycle exploring, or on a lake fishing (by myself) or involved in very physically demanding competitive sports. I guess that was their decision and it didn't kill me. I knew I was lucky because there were quite a few diabetic kids whose parents did not give them the same amount of freedom as mine.
It's too bad there wasn't more attention paid on the parent psychology of children with diabetes. That's extremely important in my opinion. I also went to diabetic kids camp for 1 month intervals - it basically taught me about being as active as anyone can be without running a high risk of low blood sugars etc.
I'm much older now - 55 - still living life to its fullest like it's one big adventure. My daughter doesn't have diabetes - but she has a dangerous job in the Navy and is often in very risky situations - I used to worry my fool head off but have learned not too anymore because it wasn't doing me any good. I suspect your parents worry about you too much. So having said that, I would suggest you try to engage them in conversation and ask them how they feel about you having diabetes - a good starting point for discussing your need for greater independence.
Good luck - I think it's tough for parents too