The word "insane" is usually reserved for a person who isn't able to function on their own, someone who needs constant care and attention. If a person has a hallucination because they took LSD they wouldn't be thought of a "insane" - mostly because it is temporary. But if someone had those hallucinations constantly - weren't able to connect with reality at all - that would commonly be seen as a state of insanity. The psychological community doesn't really have an agreed upon definition - but they tend to use the word as meaning a state where the person hasn't sufficient grasp of reality to function. The DSM has no such category and no definition for "insane" and the APA only lists the legal definition of "insanity."
Gender dysporia is that state of being unhappy with one's physical gender. That isn't a hallucination. That person know what sex they are physically, they just don't like that. Hallucinations are a break with reality at the perceptual level - it is seeing something that isn't there, or hearing something where there wasn't a sound. If that is a sustained condition it is clearly a very serious state. Transgender people "feel" like they are the opposite sex from their genitals - a feeling, not a hallucination. You can see that since they are unhappy about their physical sex, and that isn't a hallucination, that they aren't out of rational control. On a less exotic scale, you can imagine a person who feels like they really are a slim person stuck in a body that is 20 or 30 pounds overweight. They look in the mirror and they see the fat and they don't like the fat (they are dysphoric about that), and they don't hallucinate a visual image of a skinny person. If we took this to more of an extreme we can imagine such a person seeking cosmetic surgery to have the fat removed. And the surgeon should be seeing if the person is unrealistic in their expectations before agreeing to the surgery. Do they think that it will make their life perfect? If so, a surgeon would send them for some therapy first (but they aren't insane - maybe just neurotic).
Because it is a statistical manual, I have to wonder what objective standards (if any) exist outside the DSM to which psychiatrists can point as "real" or "not real" when evaluating clients for their adherence to reality or departure from reality, especially in regards to religious precepts or even scientific notions outside the mainstream.
There was a brilliant idea behind the DSM. Remember that at one time, not so long ago, there were as many as 400 different theoretical orientations. Each one saying it was the best model for understanding the human mind. Freudian, Jungian, Existentialist, Behavioralist, Cognitivist, etc. And each one with its own set of therapuetic techniques. The idea behind the DSM was to get an agreement among a majority of good practitioners on the symptoms of disorders. That is, what would you see that would be common to all depressions of a kind? What symptoms would be common to all clients who report panic attacks? What symptoms would distinguish a narcissistic personality from all others? They specifically left out any theory on the psychological model, and the theoretical description related to the cause, and they left out any description of treatment. They left all of that out because there was no way to get agreement. But they could get a high degree of agreement on clusters of symptoms and the name to associate with them. Symptoms are observable and can be objectively described. That makes it possible to have a name for a set of symptoms and thereby gather information on change, on treatment effectiveness, statistics, etc. A bridge between all the different theoretical orientations.
If you're interested here is some more info on the DSM (DSM III and IV - I'm not crazy about the V).
It is Multi-axial: That is, they divide the complete diagnosis up into 5 axis (important dimensions that can relate to the diagnois)
Axis I: Clinical Syndromes: This is the heart of the diagnosis, like schizphrenia or a phobia or major depression.
Axis II: Developmental Disorders and Personality Disorders (these are the background, if they exist, against which an Axis I disorder might be at work. For example someone might have a sociopathic personality disorder (Axis II) ever since they were a child, but they are in a hospital for severe substance abuse (which would be the Axis I diagnosis). Axis II are almost always from childhood and of one of two kinds: personality disorders, and developmental disorders.
Axis III: Physical Conditions. These are included if they play an important role in creating or exacerbating Axis I or II disorders. It gives a more complete picture of the client's situation (when a physical condition applies).
Axis IV: Severity of Psychosocial Stressors. This is just an indicator of the degree of stress the person feels relating to their personal life or career. The therapist is looking for any major events like loss of a job, divorce, death in the family, etc. Stressors can cause or exacerbate Axis I or II conditions.
Axis V: Highest Level of Functioning. It is important to have a sense of how well the person is functioning. Are they doing well in their career or work life or school? How are they doing in their relationships? This is important to know because some diagnosis would be totally inappropriate for a person who is high functioning. And if a person is functioning at a very low level, that is an important clue when looking at different diagnosis.
Next, the diagnosis are divided up into related categories like mood disorders, sexual disorders and dysfunctions, sleep disorders, substance related disorders, etc.
Then in most of those categories, there are a number of Axis I disorders. For example, Mood Disorders include Bipolar disorder, Major Depressive disorder, and a couple of others.
Under Major Depressive Disorder you get diagnostic criteria like this:
Must exhibit 5 or more of the following 9 symptoms:
A) Must report a depressed mood that occurs every day and for nearly the entire day.
B) Markedly diminished interest or pleasure in all, or almost all activities every day, for nearly the entire day.
C) Significant weight gain or weight loss not part of an intended diet (5% change in wieght in a month or less)
D) Insomnia or hypersomnia
E) Psychomotor agitation or retardation (observable by others)
F) Fatigue or loss of energy
G) Feelings of worthlessness or inappropriate guilt
H) Diminished ability to think or concentrate or indecisiveness
I) Recurrent thoughts of death.
(I've summarized these to a degree. And there are about 4 pages that describe each of key items above - i.e., what they look like to the therapist.)
Then it has differential diagnosis tips to help separate out normal bereavement, mistaking dementia in older clients from depression, ADHD, a depressive cycle that is actually part of a Bipolar disorder, depressed mood caused by physiological effect of a drug or substance or withdrawl, etc. This is like a medical doctor being told by a patient that they are having headaches and the doctor needing to rule out brain tumors, trauma induced brain injury, meningitus, allegies, stress, etc.
The whole section on Major Depressive Disorder is about 7 and a half page in length. The parts I haven't shown are the very rich and detailed descriptions of how the different symptoms appear to the therapist. (E.g., "Individuals with major depressive disorder often present with tearfulness, irritability, brooding, obsessive rumination, anxiety, phobias, excessive worry over health, and complaints of..." and so forth.)
Mostly, the DSM helps a therapist look more closely at everything being presented, think about what they are seeing more clearly, and avoid making a mistake in understanding what they are seeing. No therapist would want to start helping a person they thought to be depressed when that person should be referred to a medical doctor for treatment of a serious medical problem that was causing a few depression-like symptoms.