Obvious as it may sound, people with authoritarian beliefs hiding behind free speech actually consider it as a weakness akin empathy. It allows losers like them to amplify their reach despite not being in power. They abandon their “free speech absolutist” postures the moment they think they are in power.
It sounds ironic, but that’s only if you adhere to an almost caricature-like (or surface-level) view of what a Nazi is.
Of course, it’s better to refer to them as Fascists – that’s the more accurate term that fully refers to both of those groups. It’s just that “Nazi” is the more recognizable term to the layperson.
Fascism is slightly more diverse and thus adds more opportunities for apologists to relativize. Hence the specific choice.