I've mixed feelings. Many professions deal with being filmed, many teachers are already filmed alongside students in schools if not often with a microphone recording what is being said, and this topic does need to pushed and discussions happened and - while I've little hope for it - to reach clarity out of the conflicting mess schools are dealing with on this topic. And yes, this individual teacher screwed up in how she spoke to the students and students need ways to blow the whistle too.
On the other hand, there is context missing and yes, teachers have a responsibility to correct bullying even for things like claiming to be a cat and yeah, it sucks to be put on blast online with those who are meant to be supporting and clarifying this with teachers being conflicting in making it statutory guidance that the content be integrated but also recommending resources that use standalone lessons and units which goes against the guidance, and also at times saying those recommendations no longer count...it's a mess.
Many, many cultures outside of modern western civilisation have more than two genders.
And many, many don't. It isn't a western vs everyone else thing, there is variety all around in how social roles develop. The broad brushing of other cultures doesn't help.
Some cultures traditionally have more than two social gender roles including ones for an adult male who takes on a mostly feminine presentation and role, ones for adult females who take on mostly masculine role and presentation, and mixed roles. In cultures with this, they are all about responsibilities and what others can expect from you and in many of them, those beyond man and woman were connected to what were culturally viewed as physical and/or social abnormalities. There is no traditional ones where there is a complete swap, where someone of one sex becomes entirely the other's social role and expectations.
The concept of gender being an internal intrinsic identity is entirely modern and started in Western academia alongside what we now call scientific racism where there was an obsession with putting everyone into boxes. This is where the terms trans and cis - along with many others that didn't gain popularity - comes from: transvestite and cisvestite, defining people by clothes associated with their sex.
There have always, always been more than two genders. Sex and gender are often linked but not always the same
They aren't 'often linked', they are linked from their origins in the social sciences. Gender originally was a linguistic term - feminine and masculine and neuter. This was much later applied within the social science and in feminist activism to discuss social roles, behaviours, and expectations by sex.
Then we hit the 1950s and John Money who had the theory that gender and identity was entirely external but became internalized over childhood, did some horrific abusive experiments on children in the footsteps on Kinsey, and people died.
Using his language, things have swung the other way to the concept that it's an entirely internal individualistic intrinsic identity to be discovered and the more recent attempts to decouple it from sex and social roles. This has in rather culturally imperialistic ways been spread and applied onto cultures where the internal identity of gender is a very inaccurate way to describe them. It's applying western ideals of identity onto them and it has really screwed up how we discuss gender systems because we treat that one as the as the default. It's not unlike the reformation where religion went from a code of conduct for how to behave with deity and people to internal beliefs and was then applied to other faith systems in a way that still makes religious literacy difficult when the internal Christian framework is treated as default.
There are multiple genders. There always have been. Nobody ever manages to actually refute this, and people who try generally end up resorting to insults.
There are multiple gender systems, many different systems across the many cultures and times.
Some of them have two genders, no more can be applied within them and it be the same gender system. Some gender systems have 3 or 4 or more - again, we cannot apply more or less and it be the same gender system. Until recently, those were all about the expectations and responsibilities socially applied to people based on sex.
This has moved very recently in some places to an internal concept with no responsibilities attached - that is very new. It's actually difficult to call non-binary and some variants of transgender genders in the social sciences sense because they aren't roles, there are no social expectations or responsibilities, they're just identities. There has been a decrease in those social expectations on women and men in many Western cultures, but it's still there in a way that it is not for recent identity concepts using the gender label.
The concept of internal individualistic intrinsic permanent identity is not a universal concept. That any such thing exists is one that has been argued for a while and likely will forever more. The trans/cis gender system is a modern western gender system that is among many others and in its most recent variant relies on that concept that we all have this internal identity and this is a defining part of an individual. It has its uses as a lens some people use, but should not be universally applied and I don't think should be used as a representation of genders in wider culture. It's part of why there is push to use gender diverse as the umbrella term with transsexual people, transgender, and non-binary people as types of gender diversity.