Would it not be more correct to say that the Church has no teaching on gender identity as distinct from biological gender, because the experience of a small but significant number of individuals proclaiming dissonance between their body and psychic gender is a new phenomenon? 

I you agree with that (and I assume you will, Tridentinus, since it is pretty hard to find reliable statements about something before it exists), then what we have here is the standard reply of just about any inherently conservative institution (and I am happy my Church is an inherently conservative institution) to anything new -- condemn it (I am not happy that my Church follows this standard reply). 

Now is the time for the Church NOT to reply, but to ponder, study, reflect, pray, beg for guidance, and perhaps in a few decades when the picture is clearer, proffer a few words of encouragement in making sense of a challenging new reality; and then perhaps in a few more decades suggesting some moral guidance.