Are Public Schools Teaching Kids to be Moral Nihilists?

Justin McBrayer, wrote this interesting piece for the New York Times. He argues that there is a misleading distinction embedded in the common core standards when it comes to teaching students the difference between facts and opinions. We’re all probably familiar with the drill. Students are given a list of sentences and asked to distinguish the facts from the opinions. Things that can be proven by science or simply observation are supposed to be labeled as the facts and things that are more subjective (like “Ice Cream tastes good”) are supposed to be labeled as opinions.
But McBrayer’s worry is that children seem to be taught than any evaluative claim is merely an opinion and something that couldn’t be true. But if one thinks that facts are true propositions (which a lot of students likely do), then students could reason that it’s not true that it’s wrong to kill people for fun. Why? Because moral judgments are evaluative claims that children are taught to label as opinions. If there is a sharp distinction between opinion and facts, such that opinions couldn’t be true, then we have a system that might be teaching kids to be moral nihilists?
What do you think? Should we teach the fact/opinion distinction? Is it problematic to train students to think that moral judgments couldn’t be objectively true?