Something can be labeled “hate speech” when it isn’t. Then the labeling itself might be seen as a form of hate speech. The original speech might be true, or at any rate not entirely false.
If you define “hate speech” as something false, your question answers itself. But it still leaves the question: if it’s false, is it necessarily hate speech?
Also, to be called false, must it be entirely false, or is it false if it contains any falsehood whatsoever?
Is intent a factor, or only effect?
This is why definitions matter. Sometimes when you finish defining your terms, the discussion is over, because the real underlying question was only this: what do these terms mean?