Your idea about neutral bathrooms is the easiest solution. However, that's not what they want nor what the department of education is dictating. They say the kids who are mixed up must be allowed into the shower rooms, restrooms and to play the sport of the gender they think they are.
And yes, I think it is BS. These kids are too young to be that dedicated to wanting to change the cards they were dealt. Attention seekers? Possibly. However, the kids who are operating within societies norm have rights too.