Trans people, as some people may know, were not included in DADT and so are also not free to serve now that it has been revoked. Trans people usually can’t serve because in order to get treatment for transsexualism, trans people often have to be diagnosed with Gender Identity Disorder, which is a mental health issue, and which disables someone from serving.
Basically, Klinger was right, except everyone knew he wasn’t a real crossdresser; he just didn’t want to be in the war. Most crossdressers who serve do so while deep in the closet, just as many gay and lesbian service members did in the past. Even crossdressing is still grounds for discharge.