I have to call BS on some of Wright's claims in this article. In general his claims are based on research in animals, where one can do a common garden type experiment to tease out sex differences if desired. These experiments are not possible in humans, for obvious ethical and societal reasons.
"the evidence for innate sex-linked personality differences in humans is overwhelmingly strong."
In humans, sex differences in personality traits are persistent and measurable (though quantitative, not qualitative as he admits). This is not the same as innate unless one does a proper environmental control. Which is not possible in humans as discussed above.
"Sex-linked personality differences are very well documented in our closest primate relatives, too, and the presence of sexual dimorphism ... dramatically intensifies these differences... Given that humans are sexually dimorphic and exhibit many of the typical sex-linked behavioral traits..."
Wright fails to acknowledge that humans have experienced recent evolution of reduced sexual dimorphism as monogamy with biparental care has become the main mode of reproduction in the human lineage. This is similar to what happens in pair-bonding birds. If anything, we should expect that compared to other mammals and primates, humans will have less intense sex differences in behavior (much like albatrosses have fewer sexually dimorphic behaviors than do, say, peacocks).
"social justice view ... insists that humans are special in that evolution has played no role in shaping observed sex-linked behavioral differences"
A ridiculous strawman. The PoV opposite his is that there is no evidence - and really cannot be in humans - that any specific sex-associated behavior is innate versus learned. Because the experiments we would do in animals to tease these out are unethical. Most Evolutionary Biologists (including those he derides) would assume that any behavioral trait in humans is due to a combination of environmental, genetic, and gene by environment factors - but would also know as he apparently doe snot, that teasing this out is not possible.
(Note also that "sex-linked" is not the correct terminology for what he means).
I do agree of course, with his view that sex is not socially constructed.