I got my nose pierced (nostril) less than a month ago, and I do not think it presents any danger while doing gymnastics. I did some construction work a while back, and got hit in the face several times with boards (I know, I really need to pay better attention). At first I was concerned that the piercing (which is a stud) might stab me but it never did. I've come to accept that my nose will probably be broken before the stud stabs or damages it in any way. For the first few weeks it will be sore, particularly if you bump it, but no damage will occur. To who ever said earlier about getting it stuck on a trampoline, you would have to be genius. Even laying down on a trampoline, my nose has never gotten that close to it, and the studs are so small my hair doesn't even get stuck in it.
There is no real safety hazard in having your nose pierced and doing gymnastics. What your coaches are willing to tolerate is a different matter. Also, don't just get it done because your friends have it; while that can be good inspiration think about why you want it. I wanted my nose pierced for eight years, and only last month got it done; if you are unsure in anyway, I would say you should wait anyways because you can always do it later...that's what college is for (if you aren't on gymnastics scholarship)!