In many countries (including the US) there are circumstances where defamation law can create civil or criminal liability for such a claim, but yeah, usually not merely for stating it without certain other things also being true about the situation.
Conversely, there are cases in Germany where calling someone a Nazi would not lead to a fine. One very clear example:
Person A: [Unambiguously asserts a sincere adherence to Nazi ideology]
Person B: Did you hear that, everyone? Person A is a Nazi.
I'm not talking about defamation. I can understand why you would infer that. The fine I'm talking about is about "feeling insulted". There doesn't even have to be a third person present. Say someone treats you in a racist way, you call him Nazi, judge can order you to pay 400 Euros(or more depending how damaging he thinks you may have been to his feelings) for hurting his feelings. No need to have a witness prove it either. It's a purely subjective judgement.
You calling someone Nazi to shut down someone in public actually seems to work well to shut down public discourse judging from what I'm observing in Germany right now. I don't think those defamation lawsuits go anywhere(even though they should).
I was assaulted once and said this can only happen in a fascist country. The assaulter filed a complained saying I called him Nazi and I was fined for doing so, despite the fact that I never used those words. The law literally talks about this as something "hurting your honour". This law is ridiculous in its own right. It's not really related to the word Nazi at all. Which is why I called it a fun fact. It doesn't matter that I didn't say it. What matters is that the judge thought that I could have said it.
Attached is a case where someone appealed a judgement at the constitutional court of Germany because he was fined for calling a social worker in a correctional facility a "Trulla"[0]. Think of it as getting fined by the court for contempt by calling a random person a "Karen" in the US. He did say it, but it hardly constitutes an insult to someones honour. The courtcase argued that the way this law is currently used directly contradicts the rights of freedom of speech. Obviously they lost because it would set a precedent rendering this whole charade meaningless.
The way this law works is that it's undefined enough that what constitutes an insult to your honour and can therefore be used whenever someone threatens authority or if authority doesn't like you, you can be fined.
