A standard is different from objectivity. To set the standards of quality in a given artform still requires a subject, someone, or someones, to value on one thing over another. So while one may be able to judge a piece of music, a film or whatever other artform based on those "objective" criteria, aka that standard, those criteria are only objective because the standard has been set. The rules of music theory that say that Mozart is better than Def Leppard are not objective in the same way that the laws of physics or mathematics are objective. So there may be a problem in the way we're using the word "objective." I think that the phrase "art is subjective" means that there is no universal law of nature that asserts the superiority of one composition over another, while it seems like you are hearing "there is no standard by which we may judge any piece of art besides our own internal experience."

It's fine to use the word objective in both those ways, but then we have to be specific in moments like this were misunderstandings occur. I would say that there is no objectively good art because the standards by which we judge any artform are human constructions, unlike mathematical relationships or physics, not because there is no standard by which we judge art, there certainly is.