What is the proper adjective that describes some kind of music or art that is considered very inferior and not appealing to the ear (for music) or to the eye (for art)?
cacophonous Cambridge Dictionary
having an unpleasant mixture of sounds:
We woke up to the cacophonous sound of birds.
The restaurant is a cacophonous, high-ceilinged room.
For the appealing in art forms, we have:
aesthetic, n. and adj.
B. adj. 4. Of a thing: in accordance with principles of artistic beauty or taste; giving or designed to give pleasure through beauty; of pleasing appearance.
For the unappealing, we have the opposite:
(UN- prefix1 1.)
Source: Oxford English Dictionary (login required)
I offer (from Cambridge Dictionary)
strange and unpleasant, especially in a silly or slightly frightening way
Grotesque has come to be used as a general adjective for the strange, mysterious, magnificent, fantastic, hideous, ugly, incongruous, unpleasant, or disgusting, and thus is often used to describe weird shapes and distorted forms such as Halloween masks. In art, performance, and literature, however, grotesque may also refer to something that simultaneously invokes in an audience a feeling of uncomfortable bizarreness as well as sympathetic pity.
I don't know about "hurtful" but it sounds like "kitsch" is more or less what you have in mind.
art, objects, or design considered to be in poor taste because of excessive garishness or sentimentality, but sometimes appreciated in an ironic or knowing way. "the lava lamp is an example of sixties kitsch"
considered to be in poor taste but appreciated in an ironic or knowing way.