Even without Fr. Martin's seeming approval, or at least, lack of disapproval, of ballet, this character in his book was based on a real person. So if the downvotes in this thread are from someone who thinks of Fr. Martin as a modernist con man or something, this naysayer still doesn't answer my question. I wish he would.
I will allow that classically trained ballet dancers' bodies are formed in such an elegant way that it's impossible for me to imagine them in any kind of vulgar way. But there's a difference between immodesty and vulgarity. If someone has a child in ballet class I wouldn't think that would be wrong at all, as long as the classes are segregated by sex, and the parents don't intend their children to perform in public in the usual kind of immodest costumes. I can easily see this kind of ballet training as beneficial.
I would go so far as to say the well-trained (female) ballerina's body is almost ethereally sexless and almost angelic. Except for the costumes, it reminds me of a lot of religious art - very physically graceful. Ballerinas have a hard time dancing jazz, and that's a good thing.
But in my opinion the male ballet dancers - even though many of them are sodomites - still retain a great deal of their masculinity and are really dangerous to female eyes. Maybe with decent costumes; but then a lot of the ethereal quality would be lost, because it seems to reside completely in the bodies.