Basics
Obviously, this is a guide to writing with a focus on gender roles and dynamics, but as you should know, there are more ways to divide a society than there are to skin a cat. I brought up cisgender privilege before: the dark side to that is transphobia. There is also homophobia, xenophobia, racism, ableism, ageism, colorism, classism, and religious discrimination. And each and every one of these is going to have an effect on how your matriarchy’s misandry displays itself when they cross paths, hence the term intersection.
Let’s take the intersection of homophobia and misogyny in the real world for an example. There is, and has been for quite some time, the common fallacy that lesbian sex does not count as real sex, as there is no penis involved. No penis, no sex, no abomination is that line of thinking. This has the major downside of many people thinking that all a lesbian needs to be "cured" is a real man- try googling ‘corrective rape’ some time and prepare to be squicked out of your mind- but it was somewhat offset by the good side as well, that of protecting many lesbians from otherwise homophobic practices. The Victorian morality laws that imprisoned Oscar Wilde didn’t apply to women who had sex with women, but only covered men who had sex with men. The favor is still found with the men: for all that as a possible result of being outed "I may be raped" is better than "I may be raped and/or imprisoned", it's still a whole lot worse than "I may be imprisoned". If your matriarchy places no stigma on homosexuality, this won’t be an issue, but if it does then you have some thinking to do about the differences between a gay man’s life and a lesbian’s life.
The intersection of race and gender was- and really, really still is- a huge source of contention in the Women's Rights movement. Because the portrait second wave feminism painted of oppressed women was so very limited to white women that everyone else was shut out. Being on the low end of one type of hierarchy does not absolve you from abusing your position on the high end of another.
Even if you’re making up your society out of whole cloth, please, keep these sorts of things in mind, as they could affect not only your story but the way your readers take it as well. If your protagonist moves through a more deeply entrenched matriarchy on his quest, the questions you have to ask not only pertain to whether or not he identifies with the men who live there, but also if you’re accidentally invoking the specter of the White Man’s Burden if he does and then acts upon it.
Yes, this can get squicky. But unexamined privilege is a squick sandwich covered in squick sauce with a garnish of squick. Really think about it- how does your matriarchy divide itself beyond gender? Even the reimagining of Battlestar Galactica, which according to word of Ronald Moore is a homophobia, sexism, and racism free society, divides itself along the lines of planet of origin and has shades of classism. Please do your research, and ask yourself what the driving forces behind your characters- and yourself- are.
Starting Questions
1) Are there different cultures? How are they different? How does this color how they interact?
2) Are there immigrants from one culture to another? How are they greeted? How quickly/much are they expected to assimilate?
3) What norms are different in terms of gender roles in each subset of each culture?
4) Is there a stigma attached to homosexuality? How much?
5) Is there a stigma attached to transexuality? How much?
6) How much social mobility is there?
7) How does one become socially mobile?
8) How much access would a differently-abled person have to your average public building?
9) How close is the church and the state?
10) Are there any banned religions? Are certain religions encouraged or discouraged?
11) At what age would it be considered strange to still be at work?
12) What is the standard for attractiveness- pale skin, curves, and curls or dark skin, stick figure, and straight hair, to name a couple combinations?
As I said before, your narrative should include different types of men and women, rather than ones which just reflect the norms of their society. Exploring these intersections should, at the very least, give you some thought about the characters that populate your story.
Resources