Again: Do not confuse what is with what should be. They are not the same.
(TL;DR: Apologies for the length.)
There appears to be a lot of sentiment along this line of thought in this thread. I think most (if not all) of us agree there is sexism in the world. I think we also agree that the laws of the United States (and most industrialized countries) have in general been moving toward the equalization of rights between men and women as a class. I haven't seen anyone here say that this is a bad thing.
I think where most of us disagree is in what society should be, and what society should do to attempt to achieve this outcome. In order to flesh this out in my mind, I'm going to write down my thoughts, though I'm not intending to put words into anyone's mouth.
Let's call two different modes of thought with respect to what society should be Approach A and Approach B.
Approach A generally believes that "patriarchy" is an unnatural social construct that has repressed women from achieving their full potential (slavery might be a good analogy). Absent patriarchy, most occupations would be equally represented by both sexes; or, even if the occupations would not naturally be represented equally, there is a societal benefit to artificially imposing an equal representation (at least until the vestiges of patriarchy fade away). An unequal representation (whether in occupation, pay, hiring practices, etc.) is indicative that patriarchy is still influencing the potential achievement of women. Using social government intervention is acceptable to achieve equal representation in the targeted statistics.
Approach B believes that all social constructs are unnatural. Governments are instituted among men to achieve a social construct that best represents their ideals. Using the classical liberal approach, men and women should be represented in occupations in accordance with their desires and their abilities to contribute. The consumer and employer markets look at their contributions and potential ability to contribute. If governments secure rights but allow individuals to make free choices, results will tend toward the most natural and successful equilibrium(s), and hence working backward from the desired result is not the best objective (especially since so many people have different objectives).
I don't feel there is a right or wrong answer here, just different approaches. I think some societies have used more of Approach A, whereas others have tended toward Approach B.
Regardless, let's use the two approaches to take a view of one of the pieces of evidence cited by Toque. I'll use the Scientific American article, as it had a link to the peer-reviewed report which appears well-researched. The evidence shows pretty clear gender bias. Approach A would cite this as evidence that patriarchy is alive and well.
As someone who tends to take more of the Approach B, here's my take for possible reasons that the gender bias exists in that study. a) Certainly, there is some sexism in the world, which probably contributed somewhat to the results (though the study actually reported more bias occurred by the female scientists). b) Subconsciously, the scientists are probably aware the women are more likely than men to leave the workforce at some point, making a man more valuable (on average) over the long-term. c) Difference in perceived competence might be explained by the observation that females on average score better at literacy than males (
https://www.brookings.edu/research/the-gender-gap-in-reading/), so that by simple statistical inference, two equal resumes (a primarily literary task) would imply a greater probability that the male is better at science. d) Even without considering a literacy advantage, scientists can be shown to be making the optimal decision for science by multiplying the potential of each candidate times the probability that candidate will stay in the field (hypothetically, if women are 20% more likely to drop out of the field, then they should present a better resume than males in order to have similar contributions). e) Lower offers of pay to females might be considered a shrewd business decision, as women are known to accept lower pay (on average) (and yes, this is a chicken-and-the-egg riddle). f) Finally, though the effect size in the study was significant, it should be noted that with 127 participants, there was significant overlap of scores.
Conclusions: Bias, yes, but sexism, not necessarily. A subconscious bias may be toward the optimal outcome for the business or science based on the evidence available.
I'll close this incredibly long post with a similar economic example: Young males are charged more for car insurance than females of the same age, but nobody is crying sexism, because the evidence is clear that young males tend to have more accidents. I was not particularly happy about this fact as a young man (since my spotless driving record should have been just as worthy as a female's spotless record), but I accept that the different charges aren't a form of bias but rather the optimal decision by the insurance companies.