I think there's a strong, extenuating case for punishing people who deny documented, historical genocide. If you allow such an idea to become normalised and pervasive, there's a strong chance history will repeat itself eventually.
The argument is that an idea will not become ‘normalized and pervasive’ where it is allowed free, and likewise free to criticism. That, further, repressing an idea does more to encourage it.
That ideas, in a universe of free speech, are subject to the law of ‘survival of the fittest’.
This does require a somewhat idealistic assumption that humans are reasonable, but yet:
1. If humans are not reasonable enough to realize the ‘good’ ideas, then how can any human assert that they are reasonable enough to realize this? It damages the assertion that it is in fact true.
2. It requires a somewhat idealistic view of humanity indeed, but our entire concept of ethics and morality is build on a similar degree of idealism – do you see where this road leads?
We already ban speech that incites harm towards individuals and groups, as threats and physical violence amount to infractions of the penal code.
Where there's insurmountable evidence that an idea poses a genuine deleterious threat to civil order, and is backed by a particularly virulent and reality-denying strain of sophism, a society should be particularly vigilant in curtailing it.
I'm not talking about banning opinions and ideologies which are extreme, yet offer a different perspective on societal order, like fascism, Trotskyism, Maoism, etc, but those notions which aren't be subject to the normal spectrum of intellectual inquiry due to their utterly specious and harmful nature.
I very much disagree with the illegality of the first part. I would argue that where speech is but a medium for another crime – something tangible, not including a concept of ‘encouraging’ something ‘bad – it is justifiably illegal in the crime, where the speech is irrelevant: threats for instance where there is a reasonable anticipation of the ‘threatened’ crime.
I agree that society should be with the second paragraph: society should discourage it – but it should not be the realm of the law.
On the third paragraph, the issue here is the is no axiomatic difference between what you consider to be an ideology that justifies legal penance under speech, and one you don’t. It’s arbitrary. This alone is contrary to standards of law.