Familiarity may not breed contempt.
This is the take-home message from a Norwegian study, at least based on* the summary of the working-paper about the study:
We examine whether exposure of men to women in a traditionally male-dominated environment can change attitudes about mixed-gender productivity, gender roles and gender identity. Our context is the military in Norway, where we randomly assigned female recruits to some squads but not others during boot camp. We find that living and working with women for 8 weeks causes men to adopt more egalitarian attitudes. There is a 14 percentage point increase in the fraction of men who think mixed-gender teams perform as well or better than same-gender teams, an 8 percentage point increase in men who think household work should be shared equally and a 14 percentage point increase in men who do not completely disavow feminine traits. Contrary to the predictions of many policymakers, we find no evidence that integrating women into squads hurt male recruits' satisfaction with boot camp or their plans to continue in the military. These findings provide evidence that even in a highly gender-skewed environment, gender stereotypes are malleable and can be altered by integrating members of the opposite sex.
Questionnaires were given to all the participants both before and after some squads had spent eight weeks doing the same tasks in a mixed-sex environment while other squads had not. Because of the control group and because the initial assignment was random, it's pretty likely that the observed changes in the attitudes of those men who had worked and lived with women were due to that very fact.
The theory behind, this, contact theory, is one I've come across in older feminist books:
“That theory predicts that mixing groups will break down stereotypes, especially if they are given equal status and have common goals,” writes Gordon Dahl, one of the study’s co-authors and a professor of economics at the University of California, San Diego. “Men exposed to women are able to observe firsthand the positive contributions women can make to the team.”The first sentence is crucial of course, and so is, in my opinion, the clear sharing of same tasks in an observable manner. It's not enough that men and women are in close contact, the way many of us are in our homes or at least in our childhood homes, say.
The work must be shared so that the skills and effort of each contributor become evident to the others. Many traditionally female chores at home (cleaning, laundry) can become almost invisible (as work) to those family members who are not doing them when sexual division of labor is rigid, and it may be hard to value the work someone is doing if it appears to just happen in the background of life.
The study is an example where stereotypes could have a particularly strong role. I suspect that such stereotypes**, if obtained from the media or other similar second-had sources, might be pretty amenable to the familiarity solution, as long as the mixed-sex environment contains more than one individual*** of the "suspect" sex.
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* The study itself is now behind a paywall. NBER didn't use to do that!
Also note that even the initial attitudes of the participants were pretty gender-egalitarian.
** My suspicion applies to all kinds of stereotypes, including those about race or about race-combined-with-sex.
*** Having just one woman in the team would not provide a good test of this, for obvious reasons: If she does poorly, it could be attributed to her gender, and if she does well, she might be viewed as the obvious exception to her gender.