gender in Vrivmiya
Depending on how you count it, the Frithmy gender system has two categories (male and female), or three (men, women, and children and other barbarians), or four (men, children and other barbarians, sun women, moon women.) Their society is strongly matriarchal, in the literal sense of investing power in the hands of mothers - wife and husband are each other's equals, for instance, but both owe obedience to the wife's mother. To be a real man, or real sun/moon woman, it is necesary and sufficient to learn the hunter's, sun, or moon languages and undergo the relevant initiation ceremony. Someone's gender, like their lineage and most serious oaths, should be obvious from their facial tattoos, or (as in the case of children and other barbarians) the absence or incoherence of such marks.
sun and moon
Traditionally, Frithmy villages are sun villages or moon villages. Traditionally, as the bulk of their labor, men hunt, moon women weave, and sun women garden. Women inherit a portion of their mother's land to pass on to their own daughters, while men born to sun women leave their village to marry moon women and visa-versa. The women of any village, being closely related and speaking a secret and highly flexible language - the hunter's language, though capable of great subtlety, has a much more restricted range of topics - maintain its matriarchal character.
In the last few centuries this system has come under strain, and not even primarily due to the Frithmy incorporation into the Empire. The adoption of new methods of agriculture and conversion of wild lands to settled ones has marginalized hunting and demanded instead men's involvement in producing crops; and in towns, which accept all and sundry, sun/moon identity is largely stripped down to its incest taboo core (against sun women not letting their daughters bring into their house the suns of other sun women, and the same for moon) and the sacred languages are mostly whittled down to a few memorized phrases necessary for initiation.
marriage, household, slavery
In principle, bride and groom are matched by their mothers, and the consent of neither young person is not required - it is an exchange between one older woman's house and another. In practice, everybody that a marriage without buy-in between the two parties is a recipe for disaster; and the "stereotypical" script is that a young man will show off in hopes of being noticed by a young woman (without deigning to show that he's trying to court her or indeed anyone in particular), who then talks to her mother about it, who then sends someone for his mother (the least informed party of all), and if the politics of it work out - families of similar standing, a chance to see that the young people get along once they can more explicitly court - then you've got a new couple. The groom's mother gifts him a dowry to bring into his new mother-in-law's household - typically animals, since that is men's work.
In ancient days, when Frithmy society was more equal, most villages consisted of a longhouse used in common by nuclear families; with those of middle age defering to the wife's mother as long as she lived. Those kept as thrall did so only for their own life; male victims of war were killed, female victims typically from the opposite moeity excluded from the women's councils, but their daugters and sons initiated as if they were daughters and sons of the village. Those who disliked the local leadership, if denouncing them in council was ineffective, would strike off with axes to form a new village in the next patch of wilderness.
Today the longhouses, though still the center of village life, are more directly associated with particular matriarchs, and the hand of dead great-grandmothers weighs more heavily on the living. To be held as thrall is hereditary (following the mother), their lines barred from initiation - permanent children or barbarians. Feudal ties bind people into webs of obligation based on whose grandmother was a younger sister to someone else's, and in the long run to whoever happens to own the land. To fall into thralldom is more often the result of debt bondage than war captivity, and men and women alike are enslaved - though most thralls in a settlement are still female, since male labor is more lucrative in the mines that have opened up.
Ideologically, thralls are still seen as conscripted into a household as members, and cannot be sold (but can be hired out, as to the mines noted above.) They have not yet been racialized, although the process is beginning in the northern coasts of the Leviathan clan, where mercantile interests have begun importing foreign enslaved labor, and where Frithmy thralls are most likely to just surrender to their "mothers" a portion of the wages at which they are hired out.
Within moon villages there is almost no serious threat to the security of the maternal line, and so no great emphasis placed against adultery - the cause of couple's quarrels and petty village drama but not the concern of an even-keeled, rational matriarch guiding her household. Within sun villages infidelity bears more stigma, but still significantly less so than in comparable class-based agricultural societies of our own world. Nor is it especially taboo in either moiety for a young woman to bear children before being affianced; such can prove she has good fertility, but her future mother-in-law will usually insist as part of the marriage arrangements that her first child with her new groom will be the inheriting child. Widows with children from a previous marriage (children, hence, with secure inheritance rights) tend to be the least marriageable; their household either has little to offer or else proves themselves oath-breakers; and everybody knows from the heroic epics that the children of the second husband will come to blows with that of the first.
gendered division of labor
Women have the default expected labor of managing plants, creating textiles, caring for young children, instructing younger women, governance, administrative work, medicine, and fine construction. Men bear the default expected labor of managing animals, warfare, instructing younger men, gross construction, and most dangerous things.
"Adventurers" are almost always men, although an especially high proportion of them (perhaps between a third and half) grew up as girls, the gods having called them to a dangerous life.
being trans
The rules for initiation are simple: everyone who comes of age gets initiated; by default, boys become men and women become women of the same moeity as their mothers, unless a boy gets a dream that he's supposed to be a woman or a girl that she's supposed to be a man. If a child reports this, they're taught the appropriate other language and initiated likewise, in accordance with divine instructions.
Could someone lie about this? Well, on ocassion children report with regret that they haven't gotten the desired dream or that they got one that they didn't, and perhaps there are some cases where a child was in such a situation but didn't report it; certainly in most cases children get the appropriate dream if they wanted it and not if they didn't. But none of that is surprising; after all, the gods are looking out for our own best interests and that of the world, which usually corresponds to our own judgment but sometimes does not, and there's not a better method than self-report. Theoretically, however, if someone lied about such a dream and got initiated into the "wrong" gender, their becoming a man (or whatever) would have been contrary to divine wishes, but it would still have happened. If you drink a potion of weightlessness that isn't yours, that's illegal, but you'll still float. Of course, some things are clearly too ridiculous to credit - there have supposedly been sun girls who received dreams saying they are called to be moon women, or visa-versa; obviously these cases are confused or lying.
If you've already started learning the appropriate sacred language, then it's too late to back out; even if God Herself were to come down from heaven in a chariot pulled by perytons to clarify Her intent. The gods' wishes regarding any particular person are less important than their principles regarding the exclusivity of the languages.
With the hunters' language there are arts to allow a man to sire children with a sun woman; with the moon language, arts to allow a moon woman to conceive and bear children; with the sun language, arts to allow an adult to nurse; regardless of anatomy.
the sacred languages
Sun and moon are spoken by the tongue, while the hunters' language is spoken in gestures. The moon language also has a "written" form in knotwork and lacework, while neither of the others may take permanent form. Since I am a barbarian I may not know much more.
I may speculate, though, that those sly, silent men at village meetings - where they are expected to keep silent in favor of the womenfolk, all else being equal - are having a separate conversation. When I have asked them about this some said the hunters' language is ill-suited to discussing such matters and that they were just bored and using it to play a game.
The moon women also give each other gifts of cloth, plain-looking money-textiles bestowed with great ceremony. I suspect these are letters, after a fashion.
Most magic is done in these languages.
witches
Almost nobody learns more than one of the languages, and very little other than social custom prevents them; but magical mastery beckons to whoever violates these strictures. To combine the three ways! Paranoia and revulsion must buttress reason in the armamentarium of custom; therefore Frithmy villages are regularly beset by supposed attacks of witches, and order violently restored.
It is an open secret that the Basilisk Clan practice actual witchcraft, in the sense of experimentation with combining the languages for combinatorially broader magical effect; this amongst much else makes them dependent on imperial protection.