K.D.
It really boils down to the school and the requirements. If they don't allow substitutes for gym class (a dance class or gymnastics or something) then she is going to have to accept that it is a necessary part of school.
If she hated math would you consider letting her skip math the rest of her schooling? Schools look at gym as they do any other subject and it is doubtful they will let her out it. I hated it too in middle school because I was a slow and incoordinated student. I also hated changing in front of the other girls who were more developed and seemed to flaunt their bodies. They also pointed out the kids who were shy and made fun of them.
But I stuck with it (because I had to) and by high school I actually took gym as an elective because I understood by that point what the health benefits were.