Take for example the question of short vs. long hair. This is complex because it's associated with gender roles (long=feminine, short=masculine) and sometimes with religions (like Sikhism where people don't ever cut their hair). Starting with the gender question, you have cases like that of Felicia Day, who was attacked online after she got her hair cut short. Some people clearly think that short hair implies a rejection of men, and some go on to feel that women should be punished for such rejection (assuming of course that it actually is rejection and not just a personal choice). We do talk about some kinds of short haircuts as "butch," implying that they are short and masculine. Our gender presentation is an important part of our personal identities. For men there was the question of the military haircut vs. the Beatles haircut, which started out as quite scandalous even before the Beatles grew their hair all the way out long.
There's also the question of lack of hair. There is an entire industry based around bald-shaming. Patrick Stewart has spoken about how difficult it was for him to accept his baldness, which came on in his teens.
When my family went to Colonial Williamsburg, we encountered the role-players who spoke to us of very different attitudes about hair - in particular, shaving all your hair off so you could wear a wig. In the late 17th century, wigs were super-fashionable. If you were a girl, whether and when you shaved your hair for a wig was up to your father. Brian noted that in the UK, judges wear wigs, and it's a holdover from this era. Barristers sometimes wear the wigs in crown court. Class is definitely a factor involved in the decision.
In America, wigs can be worn for fashion or they can often be worn when people have lost their hair due to cancer treatment. There is definitely a baldness-acceptance narrative around chemotherapy, which is different from, but has some parallels to, the question of baldness as it's dealt with by men. In general, women who lose hair or who have thinning hair get much more shame and trouble for it. In many cultures, a woman's hair is considered her crowning glory (in the context of male gaze!) That is connected with the idea of covering hair as modesty in certain religions.
Essentially, there are a lot of critical things at stake on our hair: personal identity, cultural identity, virility, attractiveness, and social standing.
Geisha have very specific hairstyles that are held over from the Edo era in Japan. These are not the same as Japanese hairstyles from the Heian period, when it was the fashion for noble women and their attendants to have hair that flowed all the way beyond their feet. It was also important in this time period to wash your hair on an auspicious day.
Sikhs are not the only group that doesn't cut hair. For them it's a religious observance. Some Native American groups don't cut their hair either.
Some hairstyles have to do with professions. The tonsure is a haircut associated with the historical identity of Catholic monks. The topknot began as a hairstyle of samurai in Japan, but is still worn by sumo wrestlers.
Different kinds of hair have different properties and can be styled in different ways. I mentioned the film Kirikou et la Sorcière because it portrays a community in Africa with a wide variety of hairstyles uncommon to straight-haired populations. Another story where hair has a special role is Binti by Nnedi Okorafor, which just won the Hugo for best novella.
Hair can be high-stakes as a result of racism. Black people have sometimes been suspended from school or fired from a job because of wearing dreadlocks (there is an ongoing court case about this right now). There is huge pressure for Black women to straighten their hair in order to look orderly or "professional," but it's a double-standard trap. The hair becomes an excuse to enact racism. Words like "messy" or "inappropriate" can hide underlying racist motives.
I mentioned using hair in a couple of my works - first as a social distinction between aliens in Cold Words, and also as evidence of personal conflict in my novel.
In fiction, hair can be critical to your character.
Different genres can have more or less tolerance of description of things like hair and clothes. This is related to gender bias.
In the military and police, there is starting (gradually) to be more acceptance of different culturally based hairstyles.
Beards have become an issue in the Israeli Defense Forces because ultra-orthodox beards are permitted, but beards are not permitted except in that specific population.
Hair does not have to be a major plot point in order to be used to advantage in your fiction.
Thanks to everyone who attended!