It always starts like that. People agree to very sensible things. Like hate speech is bad and it’s not censorship if it’s not mandated by the government. Eventually the definition of hate or whatever it is that’s offensive is very removed from the original meaning, and now we all bear the brunt of the sensible people who with best intentions wanted to make things better.
We have two things to unpack here. First, hate speech. What is it? Who gets to decide what the word means and what is their procedure for deciding? Is the definition stable or fluid (or even very fluid)? Is hate speech universally wrong, or only wrong when issuing forth from certain speakers? If we all agree that it's wrong, then why are people engaging in it, even unintentionally?
Second, censorship. Is self-censorship not censorship? Why must the state be involved in order to censor? We're TV networks that for decades voluntarily forbade their programming from portraying homosexuals being censored or not? What is unique about state authority versus corporate authority as it relates to censorship?
"Hate speech is bad" is a very abstract statement. The sentence conveys almost no actual concrete meaning. It seems like a rational or sensible statement, but it delegates almost all of the actual work to feelings and emotions, and highly subjective ones at that. I don't find "wanna grab a cup of coffee" terribly hateful, but apparently some people do.
I get the overall sentiment of your post, and I think I mostly agree. Nevertheless, the way we stop this nonsense is to say at the beginning that it is an abstraction over extremely subjective feelings and emotion, and thus has no basis other than eventual mob rule authoritarianism.