> Hate speech is defined by Cambridge Dictionary as "public speech that expresses hate or encourages violence towards a person or group based on something such as race, religion, sex, or sexual orientation". Hate speech is "usually thought to include communications of animosity or disparagement of an individual or a group on account of a group characteristic such as race, color, national origin, sex, disability, religion, or sexual orientation".
If I may clarify, the key part of the definition is "based on something such as [a core characteristic of a person that has no relationship to the hate] such as race, religion, sex, or sexual orientation". So hating someone for doing something is not hate speech. Hating someone for what they "are" (at their "core", if there's such a thing) is hate speech.
This isn't about finding things offensive (although clearly hate speech is found offensive by most people).
I disagree strongly about whether policing speech inevitably devolves into censorship. We already police speech, for example calls to violence in the US, with no visible devolution. We also police where you can physically be, without limiting your ability to go about your life with no undue policing. The slippery slope argument without supporting evidence is lazy.