No, the comparison to Nazis is perfectly appropriate. If you don't want to be compared to Nazis, don't pick up where they left off. If you do the work of the Nazis, you are a Nazi.

You ever seen this photo before? It's often included with little context in school history books. It was one of the first major Nazi book burnings.

What history books often leave out is that this book burning was the torching of the archives of the Berlin Institute for Sexual Science. This was an early queer and transgender support and research center. They provided some of the first trans hormone and surgical treatments. The institute's founder, Magnus Hirschfeld was an early pioneer of trans studies and even coined the term "transsexual."

In 1933 the Nazis raided the institute and burned its archives. Magnus had to flee for his life to France. Many of those involved in the institute fled the country as well. And countless trans people in Germany ended up rounded up and dying in Nazi concentration camps.

https://en.wikipedia.org/wiki/Persecution_of_transgender_people_in_Nazi_Germany

This purge actually predicated much of the advancements in trans healthcare in the US. Just like how many German physicists fled to the US, many of the early pioneers in trans science ended up in the US and helped start programs here.

This has actually been adjudicated in court:

In 2022, the Regional Court of Cologne ruled that denying that transgender people were victims of the Nazis qualifies as "a denial of Nazi crimes".[127][128] The ruling was an outcome of the civil libel suit of German biologist Marie-Luise Vollbrecht, who alleged libel against the German Society for Trans Identity and Intersexuality over their response to comments she made calling transgender people not "true victims" of Nazi crimes.[129][130][131] The court ultimately ruled that she had to accept the response made to her comments labelling her as a denialist.

If you don't want to be compared to the Nazis, don't do Nazi shit.

And yes, the comparison with Amnesty is perfectly valid. Amnesty aren't themselves involved in the persecution of trans people, but they're looking the other way, just as countless regular Germans did.