There are sadly organisations that claim that the systematic extermination of LGB and indeed T people in the 30's and 40's didn't include the T, but in light of the nazis having raided, murdered and burned their way through the first institution in the world that actually took the T seriously and attempted to respect the claims of those under its care, took steps to protect transgender people from institutionalised abuse, and even coined their name, this stance is pretty hard to defend.
Transgender people who were not hought to be homosexuals were not systematically persecuted by the Nazis. The Transvestitenschein, a certificate allowing the owner to crossdress continued to be issued throughout Nazi Germany. It's use was only discontinued in the 1950s.
There is also no evidence that Dora Richter was murdered on the day in 1933 when the Nazis destroyed the Hirschberg Institute. There is no hint at all about what happened to DR. No eye witness accounts, no sighting after that night and no body was ever found.
And the Nazis destroyed the Institute not because it contained works about transvestism, but because Hirschberg was Jewish and openly homosexual. He was the co-founder of the first gay rights organisation in the world, and campaigned to decriminalise homosexuality, and raise awareness of the fact that homosexuality occurred naturally, claiming that more than 5 in 100 German men were either gay or bisexual. A claim that was seen as so injurious to the psyche of the German man, he received endless hostility for it for decades thereafter. Including viciously violent attacks, one of which nearly killed him.
Rainer Herrn, who researched whether transvestites were persecuted under Hitler writes "Where trans people could refute the accusation of being homosexual, there is no evidence of a single prosecution".
(Zeitschrift für Sexualforschung Jf. 26 (2013) 4, S. 330–37. Original quote: "Sofern Trans*personen den „gegen sie erhobenen Homosexualitätsverdacht entkräften konnten, lässt sich in keinem Fall eine Strafverfolgung nachweisen“)
Germans are bureaucrats. They documented everything people were prosecuted for. They documented and catalogued everything they did to people. Everything, even the very worst things.
There is sheer endless evidence of persecution on the basis of sexuality. There is no evidence of persecution on the basis of gender reassignment alone.
Here is a peer-reviewed 38-page paper written by Ilse Reiter-Zatloukal published in 2014 in Beiträge zur Rechtsgeschichte Österreichs (Articles on the legal history of Austria. The journal is published by the Austrian Academy of the Sciences).
The paper is documenting cases of transgender people being allowed to officially change their legal sex in Austria after it was annexed in 1938.
I couldn't find it in English, but if you can read German, it's here: sexualityandholocaust.files.wordpress.com/2018/07/transvestiten-ns.pdf