Burchard was a colleague of sexologist Magnus Hirschfeld, founder of the Institut für Sexualwissenschaft (Institute of Sexology). Hirschfeld and Burchard, as well as researching sexology and gender, worked together in activism for gay rights in Germany.
Both men sought to repeal Paragraph 175, a homophobic law which made sex between men a crime. They also co-authored research on sexology.
Burchard died in 1920, and therefore did not see the backlash against sexology and LGBT+ rights driven by the Nazis. Hirschfeld left Germany in 1930, fearing persecution. Their research was suppressed by the Nazis, and Paragraph 175 became even harsher under the far-right.