They've long confused the ideas of sex and gender being different. Though the terminology doesn't match that making it impossible to discuss the issue logically unless you spend a ton of time upfront establishing definitions and even then many will have knee jerk negative responses to the discussion and derail it.

There's no good scientific basis for their idea of "gender" it's basically about as based in scientific reality as "french fashion" or "Chinese fashion" or "goth fashion". You can go and point out a "style" similarities between them or differences and what not, but there's no underlying universal fundamental scientific basis for why a fashion sense is what it is. That is merely a social concept. They want to to try to apply that same logic to social perceptions of gender norms and ignore the elephant in the womb. Specifically, women can get pregnant, men can't, and 99% of social differences you see surrounding the separation of the "genders" is entirely due to that fact.

Now granted I believe fully that, people should have the freedom to "express themselves" via words or how they want to dress, so long as they aren't doing anything that is bad for society as a whole. If a man wants to wear women's clothing or a woman wants to wear men's clothing. That should be legal. However that shouldn't be sufficient criteria for access to sex segregated spaces as they segregated because of the aforementioned difference in biological sex not being symmetrical.

Beyond that it's like any form of self identification. You can do it. And you should be free to do it. But me and everyone else in society also needs to be free to disregard your self identification. In a less politically heated context, I've had many people come up to me claiming very loudly that they are some "expert" at some thing, usually I take this as evidence that they are not and merely trying to seek attention, but if I'm not an expert in the thing I can't exactly "win" if I call them out. But rarely they'll stumble into my field of expertise and if they are faking it, it's extremely easy to figure out, though others outside may not be so obvious.

So naturally we all are aware when self proclaimed "investment experts" and the like give you their investment advice, we know that they are doing that in a context of an advertisement, they are doing what's in their best interests, and not necessarily what is in yours. Though truth be told not everyone understands this and is very susceptible to the advertisement, and may even get very angry if you point out key problems with it.

A very similar dynamic exists with the trans issue. It's rather complicated where this is coming from, I personally see it as a mix of general progressive tendencies to seek out marginalized groups, porn addiction, commercial forces in society putting a great deal of importance on outward appearance, but it's also a failure of the conservative tendencies of society to notice the depression and disphoria of teens and properly address why they fell that way, a failure of them to properly address those few edge cases where you do need a legal process to change ones legal sex, and a general unwillingness of society at large to have unpleasant and difficult conversations surrounding such topics until it reaches a point where it can no longer be ignored.

Of course as a museum is essentially, almost by definition a propoganda vehicle for the ruling class, it isn't surprising that the content of the museum matches closely with the current political narrative. If you went into museums in the past you'd see exhibits talking about race in what would be understood now as very unscientific terms. History museums are a very easy place to see the clear differences in how they support the prevailing narrative of the ruling class. Visit the Vietnam war museum in Washington and then visit the war museum in Saigon and they'll naturally take very different approaches towards it.

A lot of this we see now especially with the public waving of the rainbow flags and the state support of LGBTQ acceptance and whatnot is merely the state using it as a propoganda vehicle and way to rile up the population into support of the governments potential entry into a conflict with Russia and China who both take very anti-LGBTQ stances.

In essence of course gay people and trans people are being used as pawns and their best interests aren't being considered. Like any issue that becomes politicized it's rarely about the issue itself or the science behind it, but merely used as a flavor to color the propoganda machine.

You see this popular science ideal recently, lots of good public speakers are the scientific voices of authority, but good solid scientific methodology and papers are almost by necessity dry and boring, and aren't well suited for our short attention spans through television or short internet blurbs. And much like with religion it ends up becoming plays to emotion and feeling. In many ways scientific reverence has become a kind of quasi state religion of a sort. Though like any religion it's subjected to the same forces of corruption and emotional manipulation. Neil Degrasse Tyson and Michio Kaku are two good examples of the face of this kind of movement. Both excellent public speakers but they invoke an emotional response in their listeners that isn't very well conductive to a productive scientific discussion. People without much scientific knowledge but who are interested in science will oftentimes parrot these ideas as mere expert opinions, and the socially skilled will be the ones who get the positions in museums and in politics. Whereas it takes someone with poor social skills and who would rather spend their time doing math that will make the actual scientific theories. I've had more than one discussion with people who get quite mad when you point out how we tend to take for granted certain ideas, like dark matter, as must being true, despite the fact we have 0 direct evidence for it. It might well exist, there is clearly a problem with our models that require something extra that we are missing. But we have no idea what that is. It may simply be the model itself is wrong. Allowing a kind of political orthodoxy in the sciences here forces the institutions into a kind of horse blinder situation then where they'll be focused on one potential while being less clued into other potentials. There is some unfortunate necessity to this system as funding needs to come from somewhere. But just as we'll scoff at some person that is trying to twist scientific observations into a theory that fits literally with the bible, mainstream scientists are also guilty of twisting their models to fit the expectations of their patrons.