When it comes to art, relativism doesn't mean art is without meaning, it simply means that the art's meaning differs from individual to individual and since we're talking about the taste of individuals regarding music, this is the relevant context.
Jordan Peterson would imo agree that the quality of art regarding opinion vs opinion is subjective, however he would likely also say that when measuring the quality of art in relation to culture, the collective, it can be viewed objectively.
i think peterson's whole worldview is founded on a denial of the traditional subjective/objective dichotomy you're presenting here, which is rooted in the essentialism of continental philosophy (basically the idea that there's a 'real world' outside of human perception, and our words are stand-ins for the essences of things in that world). he doesn't believe in an objective reality that we subjectively perceive and gesture toward through language, or at least not one that we have any access to or relationship with, but rather a 'practical reality' that arises out of the shared
a priori biological, psychological and social structures underpinning human perception and existence, guiding how we separate the world into value-laden categories. it's a heideggerian kinda philosophy, and like heidegger he talks about that practical reality using metaphysical language which pisses off atheists like sam harris who think he's redefining words like 'truth' and 'god' (and for the sake of this discussion, 'objectivity') to suit his own ends, but he feels he's using them in the only way in which they can fully serve the purpose they're intended for, or perhaps any purpose at all in the modern world. and i think he's right, because the conventional way they're used (and i'm including the objectivity/subjectivity dualism in this) leads to confusion and an inability to clearly communicate, probably because it's rooted in misconceptions about language and perception.
this kind of thinking was the basis for wittgenstein's philosophy, who made similar arguments in his attempts to rid philosophy of concepts/dualisms/etc that were based in linguistic misconceptions which caused contradictions and prevented it from achieving clarity, but i think peterson got much of it from piaget. he kinda sets this out in his convo with tom amarque if you'd rather hear it from the man himself, but i'll try to briefly map it out here. so e.g., every person begins by categorising what it perceives in basic terms like *things that will alleviate my hunger when i put them in my mouth and things that won't* *things that will cause me pain when i touch them and things that won't* etcetc, and then those categories split into more sub-categories as your differentiation becomes more nuanced, etc. and each of these categorisations is done in order to guide action: things that will alleviate my hunger are things i will therefore eat, things that cause me pain are things i will not touch, etc. and because humans are social beings that must learn to coexist, language is the next step in this categorisation process, the difference being that the utility of mutual categorisation is limited to goals that are shared between those in the conversation.
what follows is that qualitative differentiation, even at its most complex, is guided by utility (usually an intersection between utility for the individual and utility for the group), because utility is all that causes us to construct categories of good and bad in the first place. and if this can apply to ethical systems, which most peterson fans seem to agree it does, it applies to artistic canons as well; the greatest art is that which guides the individual to act in ways that are good, with 'good' meaning ways that allow one to survive and successfully navigate existence and coexist with others doing the same etc -- the stuff every sane, functional human being desires. refer to it as something like universality and distinguish that from objective truth if you wish, but peterson doesn't do that and argues against it, i think because, as i said before, he denies the utility of using those words in that manner. but yeah, this approach to judging art is kind of implicit in his insistence that everybody should read and inhabit religious texts because they contain the deepest truth.
(an aside: harold bloom makes a similar case for shakespeare, and i highly recommend 'the invention of the human' to anyone who's interested in why such a range of different eras, critics and artists have been unable to remove him from the top of the canon despite often trying their hearts out - he actually argues to some extent that shakespeare wrote the modern human into existence, evolved us into more self-conscious beings when before our psychology was far more limited, almost triggering an evolutionary leap like the monolith in 2001 or something).
as for family guy, my whole approach toward art criticism is that you can use the same basic tools to evaluate cartoons as for shakespeare or anything else, and i'm totally on board with the idea that some so-called lowbrow stuff can be great art (this is one of the many good ideas that postmodernism brought into the mainstream, btw - postmodernism as JP describes it is full of good ideas, it's just destructive and absurd to adopt as a dogmatic ideology), it is indeed often dealing with the same ol' human themes at base. so i don't fully disagree with you here, i think you're right that family guy at its best does have at least some of exactly the sort of merit you're alluding to, i just think it hits those heights extremely inconsistently and its appeal is regularly rooted in stuff like novelty, gratuitous depravity, cliché (disposable/faulty archetypes?), narcissism, nihilism, shooting at easy targets in lazy ways etc, qualities that are usually associated with with bad art because they don't resonate or illuminate in useful ways.
no idea if this makes any sense at this hour but fuck it.