One of the top-rated comments over there begins "I find this entire argument specious from the start. The phrase 'moral facts' is deliberately provocative...." I agree.
The second "I" in that is Ann Althouse. There may be some irony in her position. That is to say, she may agree that the phrase "moral facts" is deliberately provocative but think that's a good thing. (Why would someone putting an argument in a deliberately provocative way make it specious?)
It's a respectable position in philosophy to argue for moral realism and moral facts. There are people who teach ethics at universities who would disagree with you for arguing it but no would say you were being deliberately provocative just by bringing it up. That the person making the comment cited above does is telling. It's an attempt to delegitimize an argument so you don't have to actually argue against it. (Note also that the person who uses the word "specious" clearly doesn't have a clue what it means. To them "specious" is another way of saying this is obviously wrong and so are you if you believe it. That is bullying not argument.)
The piece that inspired the comment is (NYT link) here. Short version, the Common Core curriculum teaches children to treat all value claims as opinions. The writer pretty much demolishes this by showing that the distinction between truth and opinion behind this claim doesn't hold up.
The argument is advanced by Justin P. McBrayer who teaches ethics and philosophy of religion at Fort Lewis College in Durango, Colorado. You could say a lot about that. It's a liberal arts college away from Progressive Coastland. The people who teach and attend such colleges aren't conservatives but neither are they attuned to the Jesuitical style of argument that is so valued by the sort of people who read the New York Times. (I'm being deliberately provocative.) Outside of that rather narrow cultural viewpoint, McBrayer's approach to ethics is something that would evoke no surprise or shock.
There is a philosophical position and, it's a respectable one, that argues that all moral views are just opinion. It's called emotivism. It claims that all moral views amount to, "I do/don't do this and think you should do/not do too". Or, as it is sometimes put, all moral arguments amount expressions of approval or disapproval: "Yay for compassion and boo for murder."
It's rather surprising that this one moral viewpoint is implicit in Common Core curriculum. I hadn't realized that one of the objectives of Common Core was to impose a particular kind of morality on every child. (I'm being deliberately provocative again.)
Emotivism is a respectable view, meaning no one in a philosophy department will call you crazy for trying to argue it, but it is also true that, for reasons that McBrayer exploits well in his NYT piece; it is impossible to argue emotivism without linguistic incoherence. I say "linguistic" rather than "logical" because the result of trying to argue emotivism is to render the key terms we use in moral argument meaningless. (There is a huge difference between arguing that it is very difficult to determine whether any or all moral claims are true or false and simply saying that there can be no moral facts.)
It's interesting then that emotivism has become the dominant moral
view argument of the sort of people who read the New York Times. I changed "view" to "argument" because I'm pretty certain they are hypocrites on this. If an NYT reader was arguing with a rapist she would not accept even for a second his or her contention that her claim that "rape is wrong" was being just a matter of opinion and that claiming otherwise was deliberately provocative. She would treat it as an incontestable moral fact. Confronted with the example of countries where rape is not treated as a serious crime, no NYT reader would accept the claim that people in these other countries simply see things differently.
Why do intelligent people instinctively embrace a position that can't be argued for in any plausible way? I think we can get an answer to that by taking a little challenge. Open a file and type out a list of your moral facts. This isn't a test and no one is going to hold you to it. If you prefer, type out a list of things that you might consider as possible candidates to be moral facts but you are reserving your judgment about whether they actually are for now. I think you'll find that every single one of your moral facts is a rule combined with an explicit or implicit claim that anyone who happened to find your list and read it has a duty to obey that rule.
That's why the notion that there might be moral facts scares us.