Music can be objectively superior to another piece of music, for example, Beethoven's 9th Symphony is objectively better than a song I make by farting into a microphone for 10 minutes. However there is always personal preference and someone might really, really like my farting song. Should this mean objectively is obsolete? I don't think so. We don't have to be so incredibly strict on these definitions.
Can a piece of music be objectively good by itself? Loosely, yes. An album or work that has achieved (close to) unanimous praise I would consider objectively good, regardless of whether it 100% holds to the implication that everyone who hears it will like it. I don't think objectivity in music is something to get particularly worried about, it should neither allow people to feel superior to others nor should it mean that all music is created equal. Some works of art ARE just that good that the majority of people will find them appealing. That's about as objective as we can get.