The Allies imposed anti-free speech laws on Germany as part of deNazification. The Allies believed that pro-Nazi speech had to be banned in order to democratize Germany.
Eventually, other European countries criminalized "Holocaust denial." Criminalizing "Holocaust denial" were the first anti-"hate speech" laws in modern Europe.
An interesting article on the subject: As Goes the Holocaust, So Goes the West.
most of Europe’s hate-speech laws were initially crafted to imprison Holocaust revisionists and deniers.
Another, related article: Light Skin Tone.
It’s not just Holocaust denial. Pro-Nazi speech was and is treason