Hi Gymnast Girl! I'm not Anna McNulty, but I am a former gymnast and current dancer/actor and I have a best friend who is a gymnast!
Anyways, I feel both back and leg flexibility are crucial to being a gymnast, especially if you are looking to become a competitive and/or showcase gymnast. Think about back/front hand springs, handstands, stuff like that. You need back flexibility for both. Think about split jumps and stuff like that. You need leg flexibility for that.
I hope this was helpful!