Certainly there will be jobs that attract more of one gender over another. As you mentioned, biology creates a rift naturally.
In fact in Bem's latest paper (
http://comp9.psych.cornell.edu/sec/pubPeople/slb6/Dismantling.pdf), zhi mentions that in order to overcome, interupt, and break the current social sex polarizations and compulsory heterosexuality (written in 1995) one needs to sever all the cultural constructs of what sex a person is to almost every part of the human experience. Meaning that the distinctions between male, female, intergender, and all the genders are no longer dimensions that the culture is organized.
The more practical method to achieve this is set forth in the paper to , in that rather then trying to minimize and lessen gender differences, one should try to emphasize, magnify, and elaborate the gender varieties and individual differences. Magnify that gender isnt just one or two , or even three types, but rather thousands of individual and unique variations.
And the first major problem to overcome is biology. In that first the realization that sex itself comes in different hormone levels, different anatomy sizes, different chromosome variations, and a variety of genital variations. And that any variation should not be instantly corrected, hidden, and changed to "fit in", because doing so just emphasizes the false separation that uses the sexual basis as a social construct for much of cultural roles, norms, limits, rules, issues, positions, and discriminations.
Until science makes sex a more easy to correct to true gender (not just 2), until sex birth variations are not instantly corrected, and others realize that sex has variations, as well as gender and orientations, will a great number of the population of masses be able to reap the benefit of allowing themselves to enjoy the human experience without gender limits. when a person wanting the attributes (such as more physical strength, or calm hormones to care for children more) can receive or develop that biology. And the limits of biology can be broken.
Magnify gender, sexual, and orientation variations is the first key. Which can be accomplished by logic, examples, sharing experiences, using medical facts and statistics, and sharing one's own experiences and beliefs.
Just found this chart that shows gender today.

When thinking about the strides women have made I think the feminist group is one of the reasons why such progress has been made. Is there a Masculinist group(a group that promotes equal gender expression, opportunities, rights, and roles for bio born males wanting more traditional feminine behavior, characteristics, and traits) ? The men that I know have to go along and join the feminism.