In addition, societies often run on a level of "knowing" that's used, oil-like, to smooth out social interactions---that you can look at someone and know a number of things about them: their gender, their class, their profession and/or the general nature of their immediate purpose (you dress differently to go to a funeral than you do to go to the grocery store), something about their relationships, and their general willingness to share a set of standards about how people should convey themselves.
A medieval Londoner could look at any stranger and tell if they were a servant or an apprentice or a storekeeper or an unmarried woman or a housewife (and how prosperous her husband was) or a lord or a nun or a priest or whatever; if two strangers came upon each other they knew at a glance who was to bow to whom (and life was a succession of giving and receiving small bows by way of passing acknowledgment) and whether they were of sufficiently compatable status to have a conversation or seek a friendship.
People's entire constructions of social interactions RAN on this shit for thousands of years. The intricacy and the importance of it has largely dropped, but when parents freaked out in the eighties over their son's long hair or housewives in the fifties refused to step out of doors without gloves, hat, and handbag, they were running on the social programs they grew up into and being protective of a type of status and respectability that had had real consequence in their lives.
And that consequence depended on the understanding that they didn't just have those things, they were those things. A lady was someone who had the personal skill and poise and attention to detail to pull off ladylike behavior (and the money to buy the necessary quality clothing and the leisure time to put herself together); faking it would have been no more expected than that an amateur would present herself as a prima ballerina by dancing across the stage; ladies, as well as other sorts of people, were self-proven by success.
A child who's grown to teenage years learning the concepts of freedom and truth and applying them to self-expression has largely inverted the order of operations their parents have used; instead of "I am a good, respectable high-status lady and therefore I wear the proper clothing and accessories with good grooming and good poise, and express my personal aesthetic preferences within that context" they get "I feel most myself and most comfortable with long hair and T-shirts and jewelry, this is WHO I AM, Dad, why are you persecuting me?" and the rigid standards that allowed Dad or Mom to access the securities of high social status according to the mores of their generation are subordinated or dismissed entirely, to the embarrassment and terror of their parents who viewed that respectability of dress and behavior as both security and privilege were aghast that their children would so willingly reject it, when it arguably was barely REAL to their children in the way it was to them, and functions more as prison than social status buff.
The idea of dressing purely for one's own aesthetic pleasure, let alone being a whole new gender, comes across as part neglect of a very important social function, and part pure dishonesty, to someone who depends on the structure granted by standards and assigned places in the standards. A paradigm shift in which rights replace responsibilities and in which gender is understood as a social construct rather than a force of nature, is not something they're well equipped to handle, and the translations and explanations have not been as useful as they could be.
Social mores and their use are a technology, in the widest sense of the word, and a lot of old people are in their "you met your fiance OVER THE INTERNET?!!! They could be anyone, you'll be murdered!" stage regarding the ability to choose to become something other than your family status and birth assigned you.
We're saying "assigned" as in "assigned gender at birth" should be a suggestion, and they're trying to wrap their heads around it not being a rule, and what it means when an island they've stood on since birth reveals itself to instead be a really big whale.