My gym seems to allow girls to wear the shorts that are designed for gymnastics - we sell GK shorts, too. One girl (10 yrs) always gets yelled at for wearing non-gym shorts, although they ARE pretty skintight. Sometimes they try to discourage younger girls from wearing shorts, but they always let the older girls (for reasons all over this thread) so it doesn't stick. With the "Why does [best gymnast in the gym, 17yo] get to wear them if I can't?" stuff, it's hard to enforce.
I never wear shorts, cuz I'm worried they'll make bars feel different. Besides, what if I get my period during a meet? I just got it this summer after two years w/o, so I was like "WHAT. I gotta do gymnastics like this?" but then I got used to it. :-(
As for two-pieces, we ordered a lot of them last summer but wound up not letting the girls wear them. It's very hot and we don't have AC, but when the older girls wound up wearing them, the tops were too revealing. They didn't want a double standard, so nobody can wear them now. You can wear the bottoms as shorts, though.