I think this is an overly simple response to a deep problem. We are all affected by what we take in, some more than others (and certainly when we are attacked). Getting people to be unaffected (or less affected) is likely to prove untenable or impossible.
Putting the onus on the recipient also leaves us blaming the bullied. "Maybe if they'd had tougher skin they wouldn't have committed suicide."
Start taking these less seriously. Start building better functional families. You will see these problems will slowly vanish. Happy kids from happy families have extraordinary bullshit avoiding capabilities.
If it is a physical assault we need to engage the legal system.
If not, treat these as mind games. The opponent expects you to behave in a predictable manner. If you react violently or weakly, they win. Censorship is a weak move. It is very much possible that your opponent (possibly, a front for some government agency or a political party) expects you to want more censorship (you can guess the reasons).
Words cannot ruin our religion\race. If they can, our religion\race does not deserve to exist. A religion\race that needs the crutches of censorship is a weak religion\race.
I am not proposing a simple solution here, but your blithe dismissal of online abuse is comical and cruel.
This is a misunderstanding of hate speech. If leaders of a group direct harassment campaigns against another group, that speech hurts whether you "let" it or not. For example when reddit had a "fat people hate" group, they started coordinated harassment campaigns. When the subreddit was deleted, they didn't have a support group telling them that harassment was ok, and they didn't have an obvious place to coordinate even if they wanted to.
You could harass someone with ideas they agree with by spamming or other means to create disturbance in social media or other forms.
Edit: note we're not necessarily taking about the state mandating the censorship, which potentially gets into first amendment territory. We're including service providers and ToS.
I should just ignore the thousand notifications with insults, I mean I can't block them can I? That would be some awful censorship.
Can't believe you actually compared this to a dog not barking at other dogs in another reply further down, how disingenuous.