Example sentence:
He may have a personality disorder, a depressive disorder, or autism spectrum disorder.
Why is that personality disorder and depressive disorder requires an a but not autism spectrum disorder? (Or maybe I'm wrong about this?)
Because ASD is the name of a condition (and is often written with initial capitals). The other two appear to be adjectives describing (limiting) the meaning of the common noun "disorder".
Personality disorders and depressive disorders are both classes of disorders, that is, the term encompasses several more specific diagnoses. He may have a personality disorder, or a depressive disorder, but it is not stated exactly which specific personality or depressive disorder he might have. (Examples: paranoid personality disorder, borderline personality disorder, dependent personality disorder, melancholic depression, seasonal affective disorder, etc, etc.)
In contrast, autism spectrum disorder—despite being, itself, a collection of many symptoms which are not always present in any given person—is spoken of as its own specific thing. Simply saying "autism spectrum disorder" is sufficient to make clear the exact diagnosis you are referring to, while both "personality disorder" and "depressive disorder" are too broad to be used that way.
He may have a personality disorder, a depressive disorder, or autism spectrum disorder.
This sentence displays competing analogies to different structure. One structure is exemplified by such sentences as:
A. He has a disorder/a fever/an illness/a skin disease/a psychiatric condition/a fear of dogs/a cold/a tumor/a bruise/a scar.
The other structure is exemplified by such sentences as:
B. He has ADHD/COVID/pneumonia/arthritis/appendicitis/gout/schizophrenia/high blood pressure/cancer of the throat/acne.
I think the first structure is more common for conditions named with a common noun felt to be independent of formal medical diagnosis, things felt as describing discrete "objects," and things felt to be one instance of a possible repeating phenomenon. The second structure is more normal for the names of formal diagnoses, conditions felt to exist mostly on a scale of severity, and things felt to be physical mass nouns.