Like I said in another comment, you and I don't feel that way, it's really hard (for me at least) to imagine feeling like you're in the wrong body or that you do not conform to a traditional male or female gender. But that doesn't mean a person who feels this way is mentally ill. I work with people who are mentally ill in a clinician role (nurse) - I deal with people who suffer from schizophrenia, clinical depression, bipolar disorder, dissociative identity disorders, personality disorders, etc. Those are mental illnesses. Gender dysphoria perhaps is one, but that's often because of the stigma you mentioned as was cited in one of the articles.
This isn't new. Many cultures have recognized a 3rd or even unlimited gender possibilities.
Bottom line is that the way these people feel and choose to live their lives does not harm us and shouldn't concern us. People are free to do and say whatever they please as long as it does not infringe upon the rights of others.