Chomsky wrote the definitive progressive answer to all this 50 years ago:
https://libcom.org/files/chomsky%20-%20iq%20building%20block...
Still timely and fresh, especially considering that he was critiquing Herrnstein 20 years before The Bell Curve.
Because he's smart and unafraid, either of science or the truth, Chomsky never denies the possibility of a genetic component to IQ, even IQ/race. What he denies are the ideological assumptions people make about the social consequences that must follow if those findings are true - assumptions which he brilliantly lays bare and then demolishes. He also questions the scientific significance of the research - even if it is true (a phrase he uses a lot).
Since not one of his arguments depends on Herrnstein's scientific claims being false, the issue of science denialism never comes up with Chomsky. He lets his opponents have everything they "ask" for empirically ("even if it is true") and refutes them on other grounds.
This must partly be because (ironically?) he's smarter than most people (including most other progressives) and therefore wasn't about to walk into the trap the left finds itself in 50 years later - a trap which must be tightening, if an article like the OP appears in the New Yorker of all places. But there must be more to it than this. I think the progressives who find themselves having to challenge this research as false (rather than inconsequential and insignificant, as Chomsky does), actually share many of the ideological and meritocratic assumptions that Chomsky writes about - for example the assumption that wealth and power must necessarily flow to those with higher IQ. They don't want to give up this assumption because they belong to the meritocracy themselves (or are part of the class that identifies that way). Because of this, they can't accept Chomsky's argument much more than the Herrnsteins can.