It can be verified in OALD that this adjective is often disapproving.
(OALD) inveterate adjective BrE /ɪnˈvetərət/ AmE /ɪnˈvetərət/
[usually before noun] (formal, often disapproving)
(of a person) always doing something or enjoying something, and unlikely to stop
♦ an inveterate liar
♦ He was an inveterate traveller
There is nothing disapproving about the word "traveller", for instance.
A research in Google Books shows that the most frequent nouns used with this adjective are not disapproving in meaning but instead negative in meaning; out of the six in the ngram only one is disapproving (prejudice), while four connote negative tendencies (enemy, foe, hatred, hostility).
Habit (neither disapproving nor negative cases)
(ref.) He developed a handsome shaggy white coat, a quiet, well featured face, and betrayed his low origin only by one inveterate habit; carts he took no notice of, but never a carriage, small or great, appeared in sight but he ran yelping at …
(ref.) In Mr Alexander's case the habit is seen to less advantage by reason of his voice , which is hollow , and has certainly not been improved by an inveterate habit of snuff - taking in which he used to indulge
Other nouns (neither disapproving nor negative cases)
reader, talker, arguer
(ref.) Lady Rachel is an inveterate reader, an inveterate talker, and an inveterate arguer.
(ref.) He was an inveterate writer of books, articles and reviews chiefly in the fields of history, politics and biography.
(ref.) Already an inveterate actor by the time the movie was made, having first acted in his father's movie Pound at age five, Downey's role in Less Than Zero garnered him critical acclaim.
(ref.) Though now slower of gate, his eyes, intellect and reflexes remain in good order. An inveterate fighter pilot, Vraciu is still wont to practice his skills. As he drives a highway off-ramp, Alex Vraciu will on occasion get on the six ...
The case of "friend" and "enemy"
There could be as many as 76 cases of "inveterate friend" and as many as 253 "inveterate enemy".
The conclusion could be, therefore, that this adjective is not associated predominantly with nouns that are disapproving, or in other words that identify a negative trait, but instead that it is associated predominantly, with nouns that are negative in meaning (The difference must be clear: in "a distaste for raw meat" or in "a healthy hatred for Nazi endoctrination" the words "distaste" and "hatred" are not disapproving but merely negative.); What is certain is that it is far from being associated predominently with disapproving terms and far from being associated exclusively to a set comprising disapproving terms and terms with a negative meaning.