Taste is not subjective. It's intersubjective. Subjective experiences are totally located within a particular subject. For example, "I'm hungry. I'm tired. I'm sad."
Judgements of taste, on the other hand, implicate all other humans when they are made. They implicitly demand consensus in a way that is unlike any other subjective claims. This is the only possible explanation for why people will in one breath say, "it's a matter of taste, it's all subjective" and then argue about whether or not The Last Jedi is a good Star Wars movie for hours, if not days, on end. Because the truth is, we are constantly seeking consensus and we usually resort to "that's just your opinion man" when we give up and disengage. But we don't believe that, not really.
According to Kant, "a judgment of taste involves the consciousness that all
interest is kept out of it, it must also involve a claim to being
valid for everyone, but without having a universality based on
concepts. In other words, a judgment of taste must involve a
claim to subjective universality." Unfortunately, it's Kant we're talking about, so trying to understand what he meant by subjective universality is a huge headache. Still, his reasoning reflects the way people actually talk about taste better than anybody else I've read.