People argue about tastes all the time. That tastes can't be argued over is what we tell ourselves, not what we actually do. Why else would we say "he has bad taste"?
I use taste just because it's the most widely-accepted instance where subjectivism applies. But, certainly, a substantial minority will hold that for certain kinds of tastes, objectivism holds. If you think there are meaningful disagreements about taste, that makes you an objectivist. In which case, you already agree that there are facts about these kinds of things.