There are possibly two main ways of tackling the subject within a story: take the current changes that are going on, and extrapolate what will happen if those changes continue in the same direction; or look at the fictional future world as a whole, and consider how the structure of that society has come to be, and how its development has shaped attitudes in any particular area(s).
Mostly I prefer the second approach. So many factors influence societal attitudes that trying to envision one aspect without considering the others is likely to lead to discrepancies. It's also worth remembering that changes may occur differently or at different rates under different conditions, especially when populations become isolated from each other for any length of time.
Gender is ultimately a constructed difference (or continuum) anyway, as we see already in the way it is viewed in different modern and historical societies. What are female-dominated professions now, in western societies, often stem from professions that are or were viewed as more suitable for men in another time or place.[1} In the future, will we see more reversals of what constitutes women's as opposed to men's work, or will all occupations see a roughly equal gender-balance in line with societal proportions?
Then again, what if a society has a different concept of gender due to either changes in how human biology is regarded (eg to a continuum in which female-gendered biologically/genetically female is just the opposite end to male-gendered biologically/genetically male with a range of other gender, biological and genetic combinations in between) or because alien races are encountered in which gender and/or biological/genetic sex does not exist or where more than two sexes and/or genders are recognised? How/would the concept of occupations that are dominated by and/or suitable for one gender over others be regarded in these societies?
And what of trans* folk in the widest sense of that category? How will possible future societies regard those whose gender is opposed to their biological and/or chromosomal sex? What about those who reject gender altogether? Will they be regarded as just another point on a continuum, or will societal prejudices still exist?
I tend to give a lot of thought to how my characters view gender and sexuality, and I hope I can make that clear in my stories, but I suspect some authors don't. What are good and not-so-good examples that spring to mind?
[1} For example: on the way back from presenting at a careers fair (for students on a course that has swung from male-dominated in the early 20th century to female-dominated now) I read an article by a man, where the female pronoun was used throughout as shorthand for eg 'his/her', because he recognised that he was working in another female dominated occupation (this time a writing one).