Point: The structure of “transgendered” suggests action, as if it were something you were subject to – that you are a person who has been “transgendered” and that is the reason why you exist in your present state. We wouldn’t say “gayed” or “lesbianed”.
Counter-point: Other words of similar construction, like “gifted” or “left-handed”, do not imply action, or that you’re only this way because you were subjected to something.
Meta-point: “Transgendered” bothers some people and use of it will lead to this coming up and distracting from whatever you were originally talking about. “Transgender” does not pose this issue. Therefore, use of “transgender” is preferred.
All excellent points. To add a linguistic angle:
Adjectives with -ed endings tend to express emotions and feelings. “I am frightened,” “That is amazing,” etc. Adjectives with -ed were also almost always originally verbs (to frighten, to amaze). In fact, that’s why “gifted” has the -ed — it’s built of the old verb form of to gift.
Transgender is not a verb. You can’t “transgender” something. A lot of transphobes believe you can, (“These durn libbruls are gonna transgender my boy if we don’t stop ‘em!”), but you can’t.
Transgender is an adjective, though, and as Lauren pointed out it describes a “state.” Like most adjectives that describe qualities of a noun, it doesn’t take a suffix. The sky is not “blued,” it’s “blue.” The glass is not “half-fulled,” it’s “half-full”. My mom isn’t “femaled,” she’s “female.” And I am not “transgendered,” I am “transgender.”