Sounds like this thread could use a dose of non-ideological posturing that appears to be heavy in most pro and anti responses to the OP question.
There is a mountain of evidence that testosterone and estrogen have independent and differing causal impacts the brain in both structural and functional ways that are central to countless aspects of human cognition and emotion, from memory, control of attention, and spatial navigation to sleep cycles, mood, impulsive decision making, and sensitivity to external stimuli. The evidence comes from many types of studies, including tracking changes across puberty, aging, and
cyclical fluctuations, people in hormone replacement therapy, people in gender reassignment protocols, and experiments on animals. For example,
castrating male rats hinders the ability to navigate a maze, but injecting them with testosterone improves their navigation). In contrast, i
ncrease in estrogen during the female menstrual cycle impairs spatial tasks (IOW, the two hormones of opposite effects on cognition).
To deny pervasive and meaningful average differences in brain-based behavioral differences between the sexes requires denying that the sexes differ in their levels of testosterone and estrogen, and it is an undeniable fact that they do, and to a extreme degree with little overlap in the distributions.
But of course, levels of these hormones vary greatly within gender and within each person over lifespan and even time of day, and can even be impacted by learned behaviors (taking a physical "dominance" posture increases testosterone levels in both genders). Plus, these hormones are not the sole cause of variance in any of the brain-based psychological variables they impact. Thus, there is large within gender variance and overlap of the distributions, as well as notable differences in central tendencies of each group and/or differences in the shape of the distributions. The size of the between gender differences will also vary, depending upon the age of the people.
Yet, none of these qualifications negate the fact that men and women are born with a biological difference that causes largely non-overlapping levels of exposure to different hormones that in turn have well established causal impact on structural and functional aspects of the brain and their corresponding psychological variable (many of which are in turn causal determinants of outward actions and behaviors.
Of course, all the above is just the more proximal effects of different hormone levels in the bodies of males and females after they are born, and doesn't count the sizable effects on organizational brain structure due to sex differences in the fetal brain being "washed" in hormones during the first trimester (btw, unsurprisingly statistically abnormal levels of hormone exposure during this period has been causally tied to gender-identity issues, and homosexuality).
Despite all of this, how these differences relate to things as complex and multiply determined as career choice (i.e., nurses and engineers) is not at all straight-forward, and would, at most, merely dispose a person to be more or less likely to wind up in one career over another, but only to a degree that could be easily countered by experience-based factors. Thus, such biologically based differences would account for only a portion of the observed between group differences in these areas.