The fact that she finds certain beliefs deplorable can be fact checked? Surely you jest!
But she didn't refer to "certain beliefs," but to labels--"racist, sexist, homophobic, xenophobic, Islamaphobic"--that leave a lot to personal judgment. Just look at the Coates' argument in the article Piecake linked to: In support of his claim that a large number of Trump supporters are Islamophobic, he cites a survey in which 60 percent of Trump supporters reportedly have an "unfavorable view" of Islam. But what does that mean, and does it rise to the level of "Islamophobia"? (Do you believe that the central tenets of Islam are true? If not, does that make your view "unfavorable"? If so, does that make you an Islamophobe?) Coates seems to think so.
If she had referred to specific beliefs, maybe then most people could agree on whether they fit the labels used. But even that's not a sure thing. If someone gets a job promotion because of his or her race, is that an example of racism? Does it depend on the race of the person promoted and the structural and historical facts of the society in which the promotion occurs?
In the end, what we're left with is a "fact check" that has to make a value judgment as to the significance of a belief, the meaning of the label to be applied, and whether that label applies to that belief. Only once you make those judgment calls can you turn to the numbers and do what can truly be called fact checking.
See above. You're skipping the value judgments and taking the applicability of the labels as given.
You're proving my point and not understanding the things you read all at the same time. Are you really claiming that, e.g., the classification of "Illegal immigrants should be deported" as hate speech is an objective fact about the world? And what does that have to do with denying that a racist is a racist? Nothing? Nothing.