"Free speech" cannot accept or allow anything, it's a concept not an agent.
And similar to most these concepts like "laws", "right", "privileges", "restrictions" and so on. It cannot exist on it's own, but requires a social structure for it to make any sense.
Like if you are alone you wouldn't even have the discussion about free speech as your ability to say just about anything, actually only rests upon your physical and mental ability and your motivation to do so. There's no one going to stop you and the things that could or would stop you don't care or understand your concepts anyway.
So if you define "free speech" in absolute terms, that would actually be a moral paradigm that applies to yourself and literally no one else. Which could nonetheless make sense to you but is otherwise fairly useless with respect to interactions between people.
Because as a guiding principle for the interaction with other people you'd need at least some sort of social structure, communication culture, interaction, shared values etc. Like if no one knows about your laws, customs, ideas, colloquialisms, irony, ways to express yourself and your emotions and so on, how could they make sense of that and react appropriately? Whatever it is that "appropriate reaction" would amount to anyway.
So a "right" to free speech can NEVER be absolute and meaningful to other people at the same time, because at the very least it requires a consent of these other people to that concept. Which in some way shape or form requires a social connection or relation in which such concepts can be established communicated and be agreed upon.
Otherwise you're, again, free to say anything you can and want to say but there's no one who gives anything about you and your speech or rights, let alone comprehends them.
So at the very least your ability relies on your relationship with other people and their acceptance of tolerating your speech. Which doesn't just include what you say but how you're saying it. Like if you talk to people at 3 O'clock in the night you'd likely to be told in no uncertain and likely unfriendly ways to get out of their bedroom and leave them alone. Or if you scream at people and talk without giving them an opportunity to engage, they likely won't receive that well, likely chose to disengage, kick you out or otherwise show antipathy towards you, despite them maybe even agreeing with you on the issue.
In which case you're back to square one. You're able to talk but there's no one to talk to.
So "free speech" is, copying from gnasher729, not a goal, but a tool. It's the attempt to facilitate a free and open exchange of ideas, emotions, goals, hopes, fears, aspirations, concerns and whatnot. This has often several benefits, it may help the individual to see whether they are alone in their problems or not, whether there might already be solutions for their problems, whether their fears a reasonable, whether their goals are achievable and so on. It also might help with the cohesion of society because the more people talk, the more they engage with each other, mix and match their quirks to each other and develop a culture that makes a such a free exchange of ideas possible or easier and in turn might reduce lots of troubles from a lack of communication. Including in the milder domains redundancy and in the more extreme cases antagonism, hatred and violence as a result of that.
And on top of that the exchange also increases the individual and collective understanding of society, the world or whatever people talk about, shows problems and helps with finding solutions, inspires all kind of people to do all kinds of things.
And it's a vital cornerstone of a democracy or any system that aims for self-governance. Because unless you want to live in a system where some lead and some follow, you'd need everyone to be able to get on the same page on issues, to be able to speak, to listen, to inform themselves and so on, to identify conflicts and to find compromises and resolutions for them.
But again that isn't happening in a vacuum, it's within a society. At the bare minimum you need an agreement to have at least some weak or strong social bond with other people in order to have that conversation in the first place. If you can't agree on that then the entire talk about "free speech" is meaningless.
You need some common ground and then you can have an open and honest discussion on eye level where everyone is able to receive from and contribute to it, but that's not what hate speech is.
Hate speech is antagonism. And that can be more than just disagreement. Like I might not agree with everything someone else is saying, but if the antagonism gets to the point where I see their existence as detrimental to my existence... well that's no longer about speech. That's conflict. Like people pretend as if free speech would have helped them in Nazi Germany or would be a powerful weapon against injustice.
No it won't. The thing is if "a system"/people is/are ok with COMMITTING injustices, then you're either not going to be able to tell people anything they don't already know and don't care about or they will also prohibit you from talking about it and it doesn't matter if you have a theoretical right to free speech if you're barred from all platforms, mistreated and imprisoned for whatever bogus reason they want you to be imprisoned.
Like "free speech" is not really the most fundamental freedoms to begin with. While it might have an important role in facilitating a free society. You won't even have a society in the first place unless you can agree on more fundamental stuff like safety, bodily integrity, "equality" (in all it's various forms), aso. Like if you must fear for your existence and your dear life that's not a society it's a health risk. A dead person can't speak, free or not and if you fear for your life, "speech" is the least of your concerns. Similarly if society might devalue you by default idk racism, sexism, xenophobia, etc. if you're not an equal member of society your ability to speak might be the least of your concerns and your right may rest upon the equal membership within society or the lack thereof.
So no if people are fine with murder and open violence, you'd be a fool to think they would stop at speech or that free speech would be something that you could exercise if more important and more immediate rights and vital necessities are already under attack.
Don't get me wrong, speech acts can nonetheless be a powerful tool even in dire situations. Like if you disrupt orchestrated events and pull the curtain on a magic show, if you gather numerous people, then often enough their presence alone is the message and the possibility of violent resistance rings out even when the gathering itself is completely peaceful. In general if people speak out even if it means their death, then that courage alone can be inspiring, BUT that isn't "free speech", it's people speaking. It's precisely the fact that they are NOT free to speak and that they do it anyway, that is the act of resistance and often as important or more than the actual message.
So no, it's the open society, the ideas of freedom, equality and solidarity that breed ideas of free speech and free expression as a necessity, NOT the other way around. Just because everyone is THEORETICALLY able to spout whatever hateful nonsense is on their mind doesn't mean that society is free or even that everyone is able to speak. On the contrary usually it leads to the more subtle and softer voices to be marginalized drained and excluded in favor of often the worst kinds of opinions.
Like free speech and the societies that have such values should not be taken for granted there are plenty of ideas, actually usually it's just one, but it dresses in countless of gowns, which argue to value a subgroup over all the other groups, to give up universal rights and to go towards subgroup privileges and repression of "minorities" (everyone is or could be part of a minority). And to that subgroup that idea mind sound good and as long as the supports or rather doesn't actively resists such a system, it might persists regularly throwing parts of it's followership under the bus in order to maintain stability until everyone is both oppressor and few steps away from being oppressed.
So no hate speech is not, "just the expression of a different opinion". It's usually the refusal to have a conversation, the alienation from society and of minorities from society. It's fearmongering and us vs them narratives, which favor speaking about people rather than speaking with each other. Now free speech can in some ways help to mitigate that, but again it's not the free reign of hate speech, but the ability of people to talk to each other, to have discussions and to see for themselves that the hate speech, fear mongering and demonizing lack a basis in reality.
So no there is no categorical reason to accept hate speech, it cut the branch you it's sitting on. Though it's danger somewhat depends on the scale and scope. Like it might not be the end of the world if someone expresses negative emotions and isn't able to remain positive and respectful to others doing so at every moment. That happens. Often enough giving them some time to calm down and think about it, might result in apologies and normalized relations.
However that is different from ideological hatred and institutionalized distancing. When you no longer see the other as part of the team crafting the solution, but instead see them as the problem. In that case you've got an open or smoldering conflict. That's not a normal society that is a pre-cursor to a collapse. Where either these people are excluded (criminalized, deported or worse) or where you'd have a rebellion. Again disagreement is different from conflict, disagreeing people can nonetheless have the same goal and work in different ways, compete for the best solution and accept a better one or inspire and improve each other. Disagreement does not necessitate hostility.
While if there is hostility, you're in conflict mode and speech can be a weapon of war, not a means to keep peace. Like lies, deceit, disinformation, fear mongering, hate porn and whatnot can make things way worse. Like if it gets to the level where this is spread in mass media and permeate every aspect of life it will become the reality of people informed through those sources. And it will perpetuate itself if the hostility leads cuts the connections between people and entrap them even stronger within their bubbles.
So no there is no good reason, to foster those development, on the contrary it's actively detrimental to the ability to have open conversations about any topic. Because those are most likely going to happen where you do not have to face strong criticism, but where you are allowed to fail and still be respected as a member of society. So the radical opposite of allowing hate speech.
The problem is, how you'd go about it. Like what is a genuine outburst of emotions and what is hate and rage porn. What is fear mongering and what is genuine anxiety? When is the problem that you don't listen and when is the problem that the other isn't willing to talk to you in the first place? When should you stick to principles and when should you show uncertainty and willingness to compromise? Up to which point are self-serving interests to the detriment of society at large acceptable and when are they not? The thing is everyone is an individual with individual needs so being able to express them is vital, on the other hand putting them above everyone else is usually toxic, but there are various personal ideas on when it is what.
Now in the most extreme cases and when their expression oversteps boundaries of more important rights, such as again safety, security, social standing, equality etc. you could deal with that with the criminal code, but that's not really a measure you could use on bigger groups and it's one that comes with a lot of problems on it's own.
So no insulting people, attacking their mental health, their well being, their social standing, the foundation of their existence as a member of society or their membership in society to begin with, is not just "making a joke". It's an act of aggression and hostility and it's mind boggling to me how people try to brush it off by referring to an absolute right to free speech. Legal or not if you bring people to the point where they feel personally attacked you either harm them and/or invite an emotional response potentially at the same level or worse (emotional people perceive "proportional" very different).
Now ideally you don't solve that on the legal level but on the individual. It's borderline impossible to make perfect universal laws and what is an isn't offensive usually depends on context rather than the usage of particular words. However if you have organized hate groups that make it their goal to undermine society, agitate against universal rights and violate the very fabric on which free speech is build, then it can be necessary to ban those. Like what's the point of having values if you don't care about them? And if you're already willing to accept throwing people under the bus, why would you go with the unsuspecting scapegoat minority rather than with the hate group violating your values and principles?
Like that's another thing with the acceptance of hate groups you're NOT choosing between freedom and an authoritarian overreach, you're choosing between performing an authoritarian overreach and standing by while someone else is performing one. Like both is shit and you should have dealt with that a while ago within the framework of discussions rather than using force to settle a conflict, but if it comes to it, why would the free speech rights of the Nazis trump the rights to exist of countless of law abiding minorities?