Here's Rippon:
> "The idea of the male brain and the female brain suggests that each is a characteristically homogenous thing and that whoever has got a male brain, say, will have the same kind of aptitudes, preferences and personalities as everyone else with that ‘type’ of brain. We now know that is not the case."
That idea does have support, it's not a strawman. But it's the sort of idea you see from religious fundamentalists, not something any serious scientist has entertained in a very long time. People talking about prenatal testosterone, spatial reasoning fluidity, and gendered variance are not saying, even a little bit, that "everyone with a male brain will have the same aptitudes". The state of the art here is work like Joel on 'mosaic' brains, which looks at gender differences by brain region. It finds that there are many brain features gender-correlated physical differences, but these features have overlap between genders and the level of skew between different features is weakly correlated.
Here's Joel (https://www.pnas.org/content/112/50/15468):
> "Our study demonstrates that, although there are sex/gender differences in the brain, human brains do not belong to one of two distinct categories: male brain/female brain."
And a critic of Joel (https://www.pnas.org/content/113/14/E1968):
> "the authors convincingly establish that there is little evidence for this strict sexually dimorphic view of human brains, counter to the popular lay conception of a “male” and “female” brain[...]Critically, however, the conclusion that human brains cannot be categorized into two distinct classes depends largely on the level of analysis[...]In fact, an individual’s biological sex can be classified with extremely high accuracy by considering the brain mosaic as a whole."
While Rippon is jousting with the idea of strict dichotomy, researchers who reject sex differentiation concede that there are widespread statistical differences by sex. (Rippon vaguely acknowledges this too, "Of course there are sex differences", but it goes nowhere.) Other researchers are building models that can predict sex at >90% accuracy from brain-feature data. The Guardian writer implies that differences disappear after correcting for brain size, but the actual results say some significant features disappear. Even after regressing out head size, Chekroud's model retains 70% accuracy. (And of course, brain size has a strong sex correlation, so if you want to talk about real populations you wouldn't control for it.) Finally,
Finally, the story leaps to claiming adult differences are the result of socialization changing the brain. There's a lot going on here, none of it good. For one, it's the usual pop-science journalism format; the first half is study-driven, the second half applies that credibility to an unstudied claim. Do the mosaic differences exist with similar strength in early childhood? That could support or invalidate the entire narrative, and we simply don't know. For another, it makes the all-too-common mistake of conflating "not inborn" with "socialized", switching straight from physical brain structure to stereotypes without even mentioning intermediate factors like hormones. Finally, it heavily misrepresents existing research. Brain plasticity results in black cab drivers are repurposed to say that playing with Legos "very likely" produces lasting, observable brain differences. (But wait, how would gendered play be reflected in the brain? Didn't we just hear that adult men and women, despite all that socialization, don't have clearly observable brain differences? Well yes, it's not a very good article.)