These questions don't address my criticism in the slightest, but they're interesting questions on their own right, so I'll answer anyway.

Note that all things that I think are subject to revision given evidence, and reflect my best understanding at the time, and I am not taking the space to explain how confident I am in these thoughts or why. Note only that some of them I am not particularly confident in.

First, I'm here going to adopt the modern colloquial sense of the term "racism", i.e. racism is racial bigotry and prejudice, since I think that is how you tend to use the term, and as a linguistic matter, it is as appropriate of a usage as any.

(1) I think lots of things underlie racism. Most fundamentally, our natural instinct towards tribalism induces prejudice for our in-group, however that is defined, and against the out-group, however that is defined. Equally fundamentally, we have an inbuilt pattern-matching and odds-estimation capacity based on experience. In the absence of some overriding tribal affiliation, as long as we either live in racially concentrated areas, or there are substantial experiences of disparity in phenotype when conditioned on race, we will be pulled to some extent towards racism. If we somehow manage to erase race as a concept, there will still be ethnism, colorism, etc., for the same reasons, under the aforementioned conditions.

(2) I think the right wing in the United States covertly promotes and encourages racism to an extent, because it helps them reinforce their political tribal identity (which, partly accidentally, consists of mostly white people). A very very tiny sliver overtly promotes racism, but it's so deeply unacceptable in that guise that it's limited to a few crackpots (albeit potentially dangerous crackpots). The far left identitarians also explicitly promote and encourage racism much more broadly albeit usually without the violent toxicity of the crackpot right, again to reinforce their political tribal identity, but they are embarrassed to admit it so they insist on alternative definitions so that it "doesn't count". There is also a good deal of accidental or incidental racism, but I don't think that can reasonably be said to "promote or encourage"--it's just there.

(3) Focus on identity is hardly new--there have been stereotypes forever. The Ivy League (and other similar institutions of higher education) are often the source of new conceptualizations or descriptions of things, so given that and the proclivity of postmodernism to be seductive to those who are linguistically sophisticated but are not strongly empirically-minded, it's natural that these ideas would be developed intellectually in such a setting. (The lack of care for empiricism is important, because it's much easier to develop and advocate things when you're not constantly asking yourself "how big is this effect" and "how can I measure it"--this doesn't mean it's necessarily not true (though if true it's partly luck), only that development is most fervent and rapid under such conditions. Postmodernism is important because of the focus on experience over objective reality, and identitarianism is intimately related to the experience of having one or more identities.) Reporters for the New York Times tend to have received educations in such institutions, and therefore end up sympathetic to the same viewpoint, which impacts the culture of the New York Times sufficiently so that they're favorable towards that point of view. That it's specifically the NYT as opposed to some other mildly left-leaning paper is, I think, accidental, except that as a leading newspaper, NYT tends to get reporters with the best pedigrees, which tends to mean coming from the Ivy League and the like.

I do think my original charges are worth addressing, though.