An interesting question, what is trangender classified as in terms of how it affects the brain? I think illness isn't the right word for that, as it is more a different wiring than standard rather then the standard wiring short circuiting somewhere which is how I would see a mental illness (the brain breaking from the normal as opposed to being formed that way). People touched on autism and depression though as similar in being specific wirings of the brain different from the standard that are persistent and naturally formed as well, and that is a worthwhile point to mention. A mental disability or disorder might be closer, as depression and autism would probably be closer classified as, though again transgenderism is less disability so much as an alternate one in this case.
It is neurological in cause though, and a deviation from the normal healthy patterns brains usually have. It may or may not affect the quality of life of the person in the same way autism may or may not, though I can't see it as something normal for the brain in the same way autism is not normal for the brain too. This is also different from homsexuality to me, as the conflict between the mind and body in transgenderism represents an actual physical misfiring (wrong body for mind wiring) compared to just an uncommon sexual preference (still right body, right mind wiring).
I think this all does lead to the question though, that when it comes to transgender as an issue a person must address, what is the better way to address the disparity between the mind and body, by addressing it at the mind, or addressing it at the body. The body is easier to address, though the body might be normal to begin with. The mind is harder, though it is the location of where the difference occurs. It also brings up questions of how much of the identity is shaped by the wiring of the mind and how ethical or worthwhile it is to try to affect the mind to fix issues with mentality.
How transgender is classified suggests where to address the conflict between mind and body for people affected by it. So any answer there will affect how people view treatment of it. and I think that too is part of the overall topic, that it does suggest it needs treatment of some sort as it is a problem of wrong mental wiring for the body possessed, something that shouldn't be ignored if it is case going on in someone's head.
Of course, you more often get people interjecting politicization and in particular battlefield mentalities into the mix, taking the discussion and personal affronts, and these sorts of conversation and questions become a right mess to sort.