For example, "The fewer boxes you check (straight white men don’t check any)" is not only a needless snipe, but wrong. A straight white Irish Sikh in England may face 'systemic oppression' for being Irish and for being a Sikh, even while being a straight white man.
Similarly, the Marxian critique of capitalism points out that poor (straight white) labor-class men face oppression from a system set up to support rich (straight white) capital-owning men.
Bi-racial white/black people also face intersectional problems which are different from being simply able to check the black box.
Backing up a bit, I question also "Labels such as “far-right” and “alt-right,” which once might have served to strip a person of his or her livelihood and personal reputation" ... When? When did labels as applied to a person, rather than that person's expression of a re-branded white supremacism, cause that person's livelihood and personal reputation to be stripped?
I mean, we know that calling someone a "communist" had something like sort of power, but "alt-right"? Really?
As for "But a reasonable person might ask: If that’s the case, why does Quillette have an Asian woman (i.e., me) as one of its few regular columnists?", there are multiple, well-known responses - which the author mentioned, but did not address. The reasonable person should ask why did Jews act as Nazi collaborators? Was it because they were 'independent thinkers'?