"Free speech except for things I find distasteful" isn't free speech at all.
See, for example, the case of Mark Steyn, who has been harassed by Islamic extremists deploying "lawfare" techniques to silence his freedom of speech.
https://en.wikipedia.org/wiki/Human_rights_complaints_agains...
Define "hate speech".
Thought experiment: you're running the government, your definition applies. Oops, your opponents just got elected. Now "hate speech" is expanded to include "criticism of the new government".
The term "hate speech" is just a blunt instrument used by people and organizations to attack "speech I/we find distasteful".