For some people this kind of online attacking and lack of freedom to communicate (through effective trolling) may be worse than physical abuse. In the end its the brain interpreting signals and outputting pain.
In the Middle East, this kind of outsize influence might be even worse. I am no expert on Middle East politics, but I think it's fair to say that the most intolerant factions have striven to gain the most political power, in spite of the political leanings of the mass populations over which they rule.
One issue with intolerant groups is that they tend toward violence and oppression of opposing speech. The tolerant and pacifist among us can allow them to gain enough minority power to effect a political coup, which can result in a societal coup, since having political control can grant you some degree of societal control.
In such a society, espousing tolerance might carry with it the risk of violent retribution (since tolerance is viewed by the "in" group as heresy/dissent). This will cause the intolerance to spread, even if seemingly against the will of more tolerant citizens. In this way, certain ideologies can have a "toxic" societal effect. You don't need to look far in modern history to find examples. And, that's the paradox.
> As a society, you can absolutely tolerate them without the use of force, at least until the point where they actually get the majority of votes (but at that point, they are the society, and you're an outgroup in that society).
You just answered your own question
My opinion is that if there's a real threat of extreme political forces coming to power through democratic means in your society, then that society is already broken, and restricting hate speech is basically just sweeping the shards under the rug and pretending that nothing's wrong.
Suppose even we have this group that's intolerant of everyone else. But their intolerance is expressed in speech, not actions. In other words, they're saying, "you're all our enemies, and should be destroyed", but they aren't doing anything about it. Or maybe they are, but it consists of running a political party on that platform, encouraging people to vote them in.
As a society, you can absolutely tolerate them without the use of force, at least until the point where they actually get the majority of votes (but at that point, they are the society, and you're an outgroup in that society).