The Nazi regime also persecuted many LBTQ+ people during it's reign of terror. For example there is the destruction of the Institute of Sexology in Berlin. Knows as "Institut für Sexualwissenschaft" in German. This was an institute for studies about sexuality, gender and gender identify. It is believed to have been the first institute were trans people were not treated as mentally insane or disturbed (they were treated as mentally disturbed homosexual cis men and women in the rest of the world at the time and long after.)
Magnus Hirschfeld coined the term transsexualism at the institute. The library was unique and contained research, studies and theories on sexuality, including on taboo subjects like same-sex love. The library was burned to the ground in 1933 and countless history was lost together with ideas and ways of thinking that wasn't regained until moderately recent modern times.
Besides jews, other religious minorities and people with disabilities and disorders the Nazis also murdered many transsexual/homosexual people. After the fall of Nazi Germany and the end of World War II, the world vow to never again have another world war and some countries coined laws to protect minorities. And laws to protect their political systems from being corrupted by extremists again. Did the fall/aftermatch effect LBTQ+ rights as well? How? Positively or negatively?
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Sources: *https://magnus-hirschfeld.de/ausstellungen/institute/ *https://en.m.wikipedia.org/wiki/Institut_f%C3%BCr_Sexualwissenschaft
Seeing as no one else has commented and I am currently taking a break (read: avoiding) finishing a presentation, I'll provide a quick abbreviated answer.
Generally, although it was recognized that homosexuals were persecuted under the Nazis quite a few remained incarcerated or were later imprisoned for being openly homosexual. A lot of men did not disclose what they went through for fear of persecution. Both East and West Germany did not abolish Paragraph 175, which criminalized homosexuality, until 1968 for the East and a year later in the West. As historian and anti-Paragraph 175 activist Hans Joachim Schoeps noted, “for homosexuals, the Third Reich actually only ended in 1969." They had actually kept the Nazi version of Paragraph 175!
Germany also did not recognize homosexuals as victims formally until 2003, these victims were denied pensions, many lost their jobs, and there is an instance of men committing suicide because they faced the same judge who had convicted them under the Third Reich. Coffins were depicted in Freundschaft , a magazine from the time period.
Quite a few police stations also kept files of suspected homosexuals. It is important to remember that the occupying forces also had anti-homosexuality laws in place and so this informed the atmosphere at the time. There was also a lot of effort in trying to "prevent" homosexuality from influencing young boys, so although young gay prostitutes were punished, police had difficulty deciding whether they were victims of older gay men or were perpetrators, this all goes back to the Nazi ideology.
I could recommend a few books (I wrote a research paper on this exact topic for one of my classes last semester) I would recommend reading any book by Dagmar Herzog, she is fantastic. In particular Sex after Fascism, Memory and Morality in Twentieth-Century Germany is quite good and goes into a lot of detail. In addition, I would recommend the documentary Paragraph 175, there is a book by Heinz Heger called The Men with the Pink Triangle. Pierre Seel's account of his life as a gay man in France provides some interesting context, it is called I, Pierre Seel, Deported Homosexual, A Memoir of Nazi Terror. I would also recommend reading Gad Beck's memoir, his account if certainly not typical but it is definitely fascinating! An Underground Life: Memoirs of a Gay Jew in Nazi Berlin.
I hope this has been helpful!