The peoples of the Elder Wood recognize men, women, and people who aren't strictly either. Gender roles are defined in three main ways - by child-rearing traditions, by identity statements, and by laws. Here's how those break down:
Child-Rearing Traditions
Someone who gives birth to a child is the Athai of that child - their 'mother'. A feminine identity is broadly assumed, but if someone who identified as a man gave birth, they're still the Athai of that child. The Athai of a child is expected to nurse them if possible, and arrange for or perform other basic child-rearing duties. They are not expected to do so alone; rather, they are expected to act as the gatekeeper for others who want, fairly eagerly, to be involved. This expectation is not universally fulfilled, but it is commonly so; it most often breaks down in Milia communities. Being an Athai comes with community respect in the form of "Has a legacy and a stake in the future".
The primary caregiver for a child that is a man is their Marathai - their 'father'. A masculine identity is strongly expected for this title to be used for someone. Being the biological father of a child is not important so far as the traditions are concerned, though it's usually the case. Being an active presence is also required; an absent father is not a Marathai. This is because the peoples of the elder wood generally don't believe that biological fatherhood can be known with absolute certainty (but see laws, below). Being Marathai comes with community respect in the form of being considered a teacher.
Another caregiver for a child is an Eonthai; a child may have many Eonthai. These are 'aunts and uncles' in custom (and often biologically as well).
These traditions, in turn, act as the basis of a lot of gendering and gendered behaviour:
1. When tracking lineage, you trace it through your mother, not your father. Your father is a social claim; your mother is a biological fact.
2. Masculinity is largely framed in support of being Marathai; the qualities that make a good father (caring, instructive, capable, compassionate to the small) are the qualities that make a exemplary masculinity, and thus "a good man".
3. Femininity is largely framed in support of being Athai; the qualities that make a good mother (practical, clear on basic needs, able to gatekeep and select good teachers) are the qualities that make an exemplary femininity, and thus "a good woman".
4. Children are often trained with masculinity or femininity in mind based on their genitals; they have an expected identity in these terms from birth. This is weaker than a modern gender assignment, and a child who makes their identity known as otherwise early on may well recieve a broader training. Some parents also train their children more broadly as a matter of course. It is, however, still present.
In addition to this, authorities (elder councils, queens, kings) can and do declare exceptions to these rules, in all sorts of ways, especially after the death of a mother.
Identity Statements
Children don't have names; they have nicknames. Adulthood is marked by stating your name, and staking a claim to the identity you want - which may include a gender statement other than the one you were trained to, as a man or woman or neither. There are gender-neutral names; choosing one and leaving gender out of your claim will lead others to assume that they need to ask about your gendering. The only fixed expectation following choice of a neutral name is that your identity will, in all parts including gendered ones, be consistent (which is not without problems for some, of course).
Identity claims are open to some dispute - if the name you choose is the same name as someone's Athai, they might very well decide to push you on that. If someone says "I'll never remember that" when claiming a gender, that's also a dispute.
Such disputes are generally settled by bare-knuckled force, on the spot. Disputing someone's identity is an insult; in many ways, it's the insult. The conflict is always one on one; interfering dishonors the one that interferes. The interference prohibition is strong enough that shouting an identity-based insult at someone on a battlefield will normally get you single combat with the one insulted, and others clearing the way if they heard it; this happens all the time, and makes a complete hash of attempts to fight tactical battles.
Disputes over gender choice are rare in comparison to disputes over name and name choice. Conflicts over names can be actively lethal, if someone thinks a claimant is unworthy to carry a name - "Keep my mother's name out of your mouth and away from your sad self" would likely instigate a lethal fight.
The rare conflicts over gendering are almost universally fought for minor concessions or just to prove some kind of point - someone saying "I'll never remember to treat you as a woman", getting punched and asked "How about now?", and responding "Yeah, that should help" would be a funny and appropriately handled incident.
Milia Laws
Milia laws link biological fatherhood to Marathai status; they assume that the biological father not only can be but is known, and is obligated to act as Marathai.
These laws were created with the likely intent of preventing some form of "absentee fatherhood", but are widely regarded as all-around failures. The Doom Of Milus is, at least in part, political commentary on one of the strange effects of these laws - because they fix the Marathai as the biological father, they deny any other potential Marathai from taking on that role.
While they have not been technically struck down, these laws are often roundly ignored by everyone except kings and queens, who are expected to set an example. Among them, they cause all manner of trouble, which the Saesin routinely mock loudly.