Here's a five minute clip from a discussion twenty some years ago involving two philosophers, one a theist (Dr. William Lane Craig) and one a naturalist (Dr. Bernard Leikind), discussing whether naturalism can provide a ground for objective moral values.
Dr. Leikind is a relativist who apparently believes that some things, like slavery, are indeed objectively bad, but he struggles to give a reason why slavery is bad other than his own subjective aversion to it.
If naturalism is true then all moral values are subjective personal preferences, and if moral values are simply subjective preferences, like a preferred flavor of ice cream, then there is no genuine right and wrong, just as there's no right or wrong preference in ice cream flavors.
Nevertheless, the naturalist can choose to live by certain values, and most do, but the logic of his or her basic worldview should actually lead the naturalist to moral nihilism.
Fortunately, most naturalists are not logically consistent and don't follow their naturalism all the way to its logical endpoint.
If they were consistent not only would they be nihilists (see here), but they would never make moral judgments about any other person's behavior, for no matter how cruel or harmful that behavior might be, it wouldn't be morally wrong.