I cannot say for all, but I personally was in doubt which parties you are talking about. This comment I think uncovers your idea, it is far right and far left isn't it? But at first I thought you talked about parties from the article discussed: scientists sacrificing science for a noble goal of fighting social biases and scientists saying that science is more important, and the fight against biases should slow down to preserve science.
I am not sure any more about all the parties involved in the war, but some parts of it indeed seem to align with the Horseshoe theory. But then you have all the rest too, including the conspiracy theorists and whatnot. It is a dangerous game to play in this era of disinformation and propaganda.
As for science, diversity is of course a laudable goal. But it shouldn't come with a subsequent politicization of science.
PS. The actual article that NYT discussed was garbage too.