Just to clarify a point, the modern category of transsexual or the idea of gender dysphoria did not exist at the time of Hirschfield. Hirschfeld classified everyone who wasn't heterosexual as a kind of "sexual intermediary" and that included homosexuals, bisexuals, "intersex" (meaning any DSD that caused ambiguity, they didn't have genetic testing so they didn't recognize things like Turner syndrome or Klinefelter's as related to sex determination systems), and transvestites (the term he coined), which included both people who simply wanted to dress as the opposite sex, and this is the group that contained people who desired transition.
Let's not romanticize Nazi book burnings too much. I realize that this is Kiwi farms so you'll get people who claim that Christianity has been corrupted since Paul, as incoherent a statement as that is, but worth remembering that the Nazi's also destroyed texts by Einstein, and authors like Hemingway. The burning of the books at the Institute for Sexual Science was just that start of a much broader purge of psychiatric literature. Its easy to be selective about things like this in hindsight, but sorry, from the destruction of the Mayan codexes to the Bonfire of the Vanities to Nazi Book burnings, the throughline is not measured careful purging of heinous material, its just zealotry and rage.
The term transexual is from the late 40s in the US by David O. Caldwell. The work of
Harry Benjamin and
Robert Stoller are what formulates the modern understanding of transsexualism, where you see the idea of desire to transition as linked to endocrinology, and the belief that the desire is so deep seated that treating them with things like HRT was justified. Stoller in particular is the one who argues for the idea of gender identity, though for him it wasn't some magical thing that came out of nowhere:
The sense of core gender identity...is derived from three sources: the anatomy and physiology of the genitalia; the attitudes of parents, siblings and peers toward the child's gender role; and a biological force that may more or less modify the attitudinal (environmental) forces."
He also argued for transition as a last resort solution to someone who was persistently unhappy and suicidal, but only as a last resort and only for men who "had been very feminine in childhood, had never lived acceptably in a masculine role, and who had not derived pleasure from their penis". This was born out of the fact that even at that time, he had met several men in California as patients that were suicidal due to their apparent desire to be a woman. Here he was noticing what Blanchard would categorize later, that at least one type of "transsexual" was just a psychologically damaged faggot, a male with very effeminate traits that gets punished for being insufficiently manly by their childhood social environment.
It's in the 60s period in California, not 1920s Berlin, that the modern idea of trans as an identity emerges.
Thought I think modern troondom does push to induce it in people, the erotic dislocation error that produces AGP occurs as an observable phenomenon occurs far before that, and the conception of turning effeminate men in to ersatz women occurs all over the world (this is basically what every third gender category in other cultures is: the 3 genders are Man, Woman, and Girly Man*, basically every time). It is specifically in the conflation of these two things, and the creation of the idea of gender identity as in independent variable that supposedly isn't linked to sexual desire at all, that you get the current insanity that lumps together megafaggots, straight fetishists AGPs, and a whole ton of damaged women (Pooners) and not-like-the-other-girls (Nonbinary). Its essentially a category error, and it allows one group (AGPs) to use the psychological damage of the others to push for access to women's spaces to fulfill their fetish, and convinces people that gender identity isn't linked to sexuality or childhood at all. Blanchard correctly defined the phenomenon we are observing, but his ideas made the sexual element for AGP clear, so at that point the whole thing breaks from any attempt at empiricism to go live in fantasy land, because that understanding pushed against the desires of the AGPs.
I am going to differ from a lot of people here in saying that I don't think Hirschfeld or any of the others were wrong to try and document and observe, even if his understanding was ultimately very flawed. For me, this desire to pinpoint the origin of troondom to some locus of thought is wrong headed to begin with. The trans movement as it exists today is an organic, iterative process that goes through several different channels, it is not some magical corruption that emerges at a single point in modernity. And Hirschfeld, Cauldwell, Benjamin and Stoller were all recording a real phenomenon, it was a recurring desire that they named and typified. It's specifically the break with a desire to explain things scientifically (the total rejection of Blanchard despite the fact the he got it basically right and more granular than anyone else), that you get modern troonacy. Very quickly the ideas are removed from the idea of a clinical desire to treat and are reformulated by trans people themselves as a set of ideas to justify enabling the desire, and pointing out that their self-conception does not map to observable patterns of behavior is treated as "transphobic". This is my diagnosis as the core issue with all this, a break from an empiricist, anthropological or even almost ethological approach to classifying these behaviors and desires externally by observers, towards something that is defined by the sufferers themselves. Very much an inmates running the asylum issue)
*And as an aside, eunuch cults are far older than the Skoptsy of Russia. The Galli who served as priests to Cybele being probably the best example, and it was a religion that spread from Anatolia to Rome and caused enough hubbub that people worried about dudes who suddenly got an urge to cut their dicks off and join a cult. But the
Scythians seemed to have them as well, and there's the perpetual phenomenon of the beardless court eunuch across the ancient middle east.