Hi Skin,
Voluntary sep v. involuntary shouldn't make a difference unless they're using it to downgrade the type of discharge. If they're giving you anything less than "Honorable" then they're doing you a huge disservice and you should fight it. Of course, since you're committed to fulfilling your contract you should fight anyway if you still want that.
The fact that the military still considers GID a mental illness is just sad. Genderhell is right about your DD214, you'll get a category code in reference to the reason for discharge. It will be non-specific. Bear in mind that "mental illness" may be interpreted by some employers as PTSD or something similar, it won't point to GID so you'll have that to contend with.
Did you get your diagnosis from the base Mental Health office? Have you seen a counselor there? If you haven't been there, go and talk to someone. I found the doctors there were helpful personally though YMMV. The next step would be the Area Defense Counsel. If the ADC can't or won't help, contact an off base lawyer. There are firms that specialize in helping military members from getting shafted by the military. I'm assuming they're giving you an Article 15, yes? If that's the case, you don't have to accept it no matter what your chain of command might say. The alternative is a court marshal hearing which is probably not fun, but it is an option.
Also try visiting the local Veteran's Affairs office. The people there are usually all vets and they have a good idea of how to work the system.
If you are discharged despite your best efforts there are two things to do. First, get unemployment. You qualify for it immediately, it will help until you're back on your feet. Second, you have three years (a friend says you have more than that) to find problems and apply for disability, so if anything at all comes up be sure to get it into the system (see the VA for details). Of course it would also mean you could transition earlier, so getting out isn't all bad.

Whatever the outcome, you have served honorably (even if some closed minded jerks at your base don't recognize it). No paperwork can take that away. You did nothing wrong. Also, you probably deserve a hug.
::Hug::
Good luck,
-m