Karl-Maria Kerbeny coined the terms "homosexual" and "heterosexual" in a correspondence one week before Magnus Hirschfeld was born. By the time Magnus Hirschfeld founded the Institut für Sexualwissenschaft in 1919, homosexuality was a highly-researched and discussed topic in scientific/medical spheres and most central and western European countries had laws that explicitly outlawed homosexual behavior. Fortunately, the Social Democrats of Prussia controlled the government after the November Revolution, and they were against upholding the extant anti-homosexuality laws such as the infamous Paragraph 175 of the German Imperial Penal Code. This made Berlin a relatively safe place for queer folk at the time. With that safety came a queer intellectual culture, of which Hirschfeld was a significant part. You asked about what happened when the Nazis took power: by 1933, Hirschfeld was no longer living in Germany, which meant that he could not return. His Institute lasted about four months before being shut down. Hirschfeld passed away in France a couple years later. I recommend you look into this book: Charlotte Wolff's (1986) Magnus Hirschfeld: A Portrait of a Pioneer in Sexology for more information about what Hirschfeld, the Scientific-Humanitarian Committee, his writings, and the aforementioned Institute.