OK, I am NOT angry, so dont read that attitude into my response, but I would have to argue with one or two of the things that you state as givens. To the best of my admittedly poor memory, cross dressers ARE under the transgender umbrella by definition. Not that "dictionary.com" is the end all get all resource, but:
http://dictionary.reference.com/browse/transgender?s=t
The next point I would argue with you about is again based on definitions, but this time they work against me. Most definitions of transsexualism that I have seen require that the person be actively taking steps to change their body. In my humble opinion, being TS is about what you think and feel, not about what you are doing to your body, but who the hell am I to argue with the experts. . . Point being, that since I am not willing to give up my wife, my children, and my career to transition, I will remain a cross dresser - someone who takes every chance they get to spend time as female, but will not be changing my body, living full time, or transitioning. All of this leads up to your comment "since cross dressers, by definition, identify as the sex they were born as, are they truly transgender? They don't have any internal struggles with their identity. They are male, like being male and simply like women's clothing for one reason or another." This couldn't be farther from the truth for a good many of us.
If we play the "by definition" game, I am a cross dresser, but I assure you that I, and many others like me, suffer just as many internal struggles about my gender and body as those of you that meet the definition of TS, and we would probably benefit from and desire the same social support that you seek.
NOTHING is so simple, clear cut, and black and white when dealing with the transgender, that you can comfortably say or thing that a cross dresser has no place in a TS support group.
I guess that in my opinion you need to ask more than "are you a TS" or "Are you a CD", because there will quite likely be a lot of gray in there somewhere . . .