Oh, I certainly don't think that the average hard scientist's view and knowledge of humanities are much better. However, when you order academic fields by rigor and exactness, with pure mathematics on one end and humanities on the other, then as a very general rule, in order to avoid writing nonsense in your own field, you must not have misconceptions about fields that are more exact than yours, whereas knowledge of less exact fields is normally not important for scholarly work.
Thus, for example, a physicist can be completely ignorant about philosophy and humanities and nevertheless consistently produce top-quality physics, whereas a philosopher or a cultural critic who is completely ignorant of natural sciences will inevitably end up writing nonsense at least occasionally. So while both of them may have an equally distorted and ignorant view of each other's field, the latter's work will likely suffer far more as a consequence.
Regarding the Sokal affair, I agree that it's usually overblown far beyond its real significance (and physicists should also be more humble in light of the more recent Bogdanoff affair). However, I think your minimization of it is also exaggerated. Regardless of whether a journal is peer-reviewed, editors should be held responsible for what they decide to publish. I don't think the editors of Social Text would have been so eager to publish Sokal's essay if it hadn't pandered so consistently to their ideology.
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I strongly disagree here. To write meaningfully about sexual politics, you must have a model of sexual and other related aspects of human thought and behavior, and modern science has a whole lot to say about that. (Of course, the relevant science is still very incomplete and far from settled, but that makes it even more important to be knowledgeable about it, in order to separate solid insight from speculation.) If you lack that knowledge, your model is likely to be wrong in at least some ways that could be corrected by familiarizing yourself with the relevant science, and this is likely to show in your writing. Moreover, there is a whole lot of spurious pseudo-insight in this area (Freudianism and its offshoots being the most notorious example), and if you're not familiar with science beyond a high school level, you may well end up swallowing a lot of such nonsense believing it to be solid insight and incorporating it into your work.
I would agree if one is writing about Victorian sexual politics straight-up, however I was careful to specify the sexual politics of Victorian literature. For which Freudianism, notoriously wrong as it is, is highly relevant because it was enormously popular for a chunk of the time period, and did directly influence writers (more particularly in the early 20th century than the late 19th, but still). Certainly it had much more influence than post-Victorian science that the authors could not possibly have been aware of.
Which seems to me one of the hedges that postmodernism usefully offers. The decision to approach Victorian literary sexual politics in terms of the thinking of the time and to treat it as a phenomenon of that culture is, to my mind, quintessentially postmodernist.