Personal preferences would be a good examples of things that are purely subjective. There is no fact of the matter to discover about whether chocolate tastes better than vanilla. And matters of personal preference often get tangled up in our judgements about beauty. But even in the realm of beauty, many judgments capture something objective that we largely all appreciate.
Personal preferences and tastes may color people’s moral judgments as well. And we can identify a few hot button issues where this subjective aspect leads people to disagree. But then there are the vast majority of issues and cases where the objectively correct moral judgment is perfectly obvious to all but psychopaths. This looks like a situation where the subjective aspects of our experience can, in some cases, distort our judgment even as it brings us into broad agreement about the objective qualities of most things.
What needs explaining aren’t the very occasional cases where people disagree about an ethical matter. Much more surprising and in need of explanation is why we agree about what is right and wrong so routinely in the vast majority cases. Agreement about what is right and wrong is so commonplace we hardly notice. The most strident opponents about the morality of abortion will still agree that it is morally bad to torture innocent puppies, betray your loved ones, pick fights, lie in your business dealings, etc. etc. etc. The most obvious explanation is that we are perceiving moral matters the same because there is something plainly objective to see in common everyday cases of lying, cheating and stealing, etc. etc. etc.