Throwing hat into ring.
First here are a couple of references that do a good job of explaining the basic outline of sociobiology.
http://www.ship.edu/~cgboeree/sociobiology.html
http://humanists.net/pdhutcheon/humanist%20articles/12
Second I need to add a little disclaimer, I am not telling anyone to change their belief on any particular aspect of RL, just that my take on life in the 56th century goes a little like this.
As technological change and revolution in all fields of human endeavor reduces the need for direct human muscle input into task completion, the number of professions and jobs open to women, the physically weaker sex in our bisexual species, will tend to increase.
Yes I know that there are individual women out there that can mop the floor with me at will, but they are the exception, not the rule. We are a sexually dimorphic species, women are evolutionarily favored for child bearing and rearing, men can love ‘em and leave ‘em; yet both are able to fulfill the reproductive portions of our sexual/genetic inheritance as bald monkeys.
This tends to keep women out of certain fields until TL 5-7, with a greater portion of women entering the work force, able to be away from child rearing, as technology and wealth become more and more communication and information processing based (third wave technologies) These technologies tend to favor the social skills which women excel at, with their higher threshold for aggression.
This means:
Imperial citizens from low TL planets will be socially more likely to be sexist, which is defining the appropriateness of a job based on the gender of the worker.
Imperial citizens from mid TL planets will be undergoing social change that loosens the definitions of job appropriateness based on gender.
Imperial citizens from high TL planets (the majority of the Hi TL, Hi Pop which form the backbone of Imperial Citizenry) will only define the appropriateness of a job based on gender in a very limited number of fields, mostly having to do with extreme physical effort.
A corollary of this is the acceptance of homosexuality in public social spheres. (It is, was, and will be with us as long as we are sexual beings) When reduced earning power and reproduction tie a woman to home, marriage and a spouse being necessary for support; the social norm will tend to promote heterosexual, monogamous or polygamous family units. It will also tend to abhor any deviation from the norm as being detrimental to successful reproduction (The main goal of any living species).
As women’s social mobility and earning power increase the need for a supporting spouse of the opposite sex will tend to decrease. This will not mean a rise in homosexuality as an expression of genetic propensity in the population, but that its social expression will deviate less from the norm and tend to be more socially acceptable.
There is also the genetic altruism of homosexuality argument that simply states that a homosexual man or woman who contributes to the survival of their genetic relatives is ultimately contributing to their own genetic survival, even if they do not reproduce.
When you throw in cloning and high tech jobs for women the social argument for monogamous relations for social support become much less persuasive. Mix in crèches and social support for working parents as well as high tech genetic engineering or surgery to create functional hermaphrodites and you have pretty much knocked the legs out of any sexism in regards to jobs with the above exception still relevant.
I think that the marines would still tend to be masculine arm, but any woman or herm that wanted to and could pass the physicals would be allowed to join. Most of the other fields would be wide open at high tech level.
My Traveller universe is not politically correct, it is technologically correct!
As usual YMMV.