A very important figure in LGBT rights was Magnus Hirschfeld.

Hirschfeld was a MD who founded one of the first, if not the first, gay/LGBT rights organisations, "Wissenschaftlich-humanitäres Komitee" (Scientific Humanitarian Committee) as early as 1897.1

Magnus Hirschfeld coined the term "transsexualism" (now we use the term transgender instead) and wrote a book on transgender people and transvestites.

Hirschfeld also founded the Institute for Sexual Sciences (I believe this was the first sexology research institute in the world) in 1919. This institute helped recognise LGBT identities as legitimate, rather than sexual deviance or mental illness.

His stance on LGBT rights was always controversial. Here is an example of a caricature as early as 1907, when Hirschfeld campaigned to decriminalise homosexuality.

Magnus Hirschfeld was an Ashkenazi Jew, had a liberal political stance, and was a gay man himself, so was often under fire from nazi media.

Here is a specifically antisemitic caricature from 1929.

In the 20s his committee meetings were broken up by nazi sympathisers, and he was physically attacked and gravely injured. The attack fractured his skull and his death was mistakenly reported in a newspaper2

As you assumed, the nazis destroyed the institute and burned the archives in 1933 - you can see a contemporary (English language) news clip and picture of the raid here.

Hirschfeld had left for a book tour to Europe and America in 1932 - he never returned to Germany and settled in Switzerland and later France, where he passed away in 1935.

Edit: I just looked up the film date and presume you are talking about Anders als die Andern (Different from the Others) when you mention the 1919 film - Hirschfeld was also a co-writer on this film, but I have not personally seen this film and can't comment on it, which is why I left it out of my comment otherwise.