I can’t even wrap my head around the person who doesn’t want anybody trans in their aerobics class, nor in my years writing a fitness column have I ever seen “female-only” as a spec. This is a hokey, made-up scenario. Those crop up a lot.
I think she is hiding behind the meaning of the words women and female.
In her world (definitely not mine) women includes women and men who say they are women. So a women-only exercise class includes female adults and male adults.
In her world female-only is different because it excludes male women.
So if she has only come across women-only classes she can pretend that it was never synonymous with female-only classes.
Obviously, to the general public women-only means the same as female-only.
It's why it's so important we only use the word woman for women as anything else leads to confusion and loss of women's rights.