Reviewing the background of hate-speech policies at the international level, Jacob Mchangama notes an interesting dynamic that one encounters in other areas of human interaction:

Human-rights agencies are sympathetic to hate-speech laws partly because international human-rights con­ventions at the United Nations were instrumental in globalizing and mainstreaming them. The U.N.’s International Cov­e­nant on Civil and Political Rights (ICCPR) recognizes a right to freedom of expression, but it also states that “any advocacy of national, racial or religious hatred that constitutes incitement to discrimination, hostility or violence shall be prohibited by law.”
The first working draft, as early as 1947, included only incitement to violence — universally recognized as a permissible ground for restricting freedom of expression — but the Soviet Union, Poland, and France wanted to include incitement to hatred as well. This was met by resistance from most Western states; the U.S. representative, Eleanor Roosevelt, hardly a libertarian, called the prohibition of incitement to hatred “extremely dangerous.” The U.K., Sweden, Australia, Denmark, and most other Western democracies opposed the criminalization of free expression, counseling that fanaticism should be countered through open debate instead.
But these objections did not impress the majority of the U.N.’s member states — Saudi Arabia asserted at the time that Western “confidence in human intelligence was perhaps a little excessive” — and the “incitement to hatred” language was kept in. So it was that a coalition of totalitarian socialist states and Third World countries, many of them ruled by authoritarians, succeeded in turning a human-rights convention into an instrument of censorship.

That’s a sort of general broad-brush view of totalitarians’ leveraging of notions of freedom; Mchangama subsequently offers a more specific instance:

The Holocaust was still fresh in the minds of those who drafted the hate-speech-related U.N. conventions during the 1950s and ’60s, and fresh memories of Nazi atrocities helped them to get those conventions passed. A lax attitude to Nazi propaganda, their argument went, had helped pave the way for Nazi rule and the annihilation of millions of Jews. But justifying hate-speech laws with reference to the Holocaust ignores some crucial points. Contrary to common perceptions, Weimar Germany was not indifferent to Nazi propaganda; several Nazis were convicted for anti-Semitic outbursts. One of the most vicious Jew-baiters of the era was Julius Streicher, who edited the Nazi newspaper Der Stürmer; he was twice convicted of causing “offenses against religion” with his virulently anti-Semitic speeches and writings. Hitler himself was prohibited from speaking publicly in several German jurisdictions in 1925. None of this prevented Streicher from increasing the circulation of Der Stürmer, or Hitler from assuming power. The trials and bans merely gave them publicity, with Streicher and Hitler cunningly casting themselves as victims.

A modern tendency of people to try to be “on the right side of history” comes to mind in this context, because we’re too inclined to count the wrong things as culpable. For simplified example, we see in retrospect how hate speech against a group contributed to the atrocities of the Holocaust, so we’re apt to consider hate-speech laws to be a reasonable preventative measure. But this creates the opening for those who wish to silence ideological opposition to present themselves as victims and to cast their defense as a foresighted avoidance of potential atrocity.
Imagine a personification of two forces in history — we’ll call them, I don’t know, Good and Evil. The intent of Evil isn’t to be mean or unpleasant, but to harm others, or at least to treat the harm of others as inconsequential. Sometimes that intention is accomplished by lamenting Evil’s own strategies so as to benefit from the backlash against them, while painting Good with the tainted brush.