Yes, there is such a thing as hate speech. The ideal of free speech is just that - an ideal, and like every freedom at some point it rubs against the reality of how a society functions, at some point you need to weigh the cost of that freedom against the benefit. You even say it yourself, with you it's direct calls to violence, and the next reply correctly points out that actually, even before calls to violence there can be problems. Whether or not you go on to say "... and therefore saying these things is illegal" or you go on to say "... saying this stuff is kind of not on and if you're going to say it don't say it in here" is kind of a side question. The speech still exists and in the real world we have all sorts of moderation, social contracts, and yes law to deal with it.
An argument often given in support of a pure perfect freedom of speech is that of the marketplace of ideas: if you let people say whatever they like, they'll discuss and over time the good ideas will win out over the bad. This is one of those imaginings of the world that's so naive it's almost funny. Nowhere outside of a polite debating society does that happen. In reality, people come to information with biases and flaws and a lot of really really easy to understand (but factually wrong) ideas persist no matter how long they're explained. (To take a benign example from another thread: despite the scientific proof to the contrary the uptick in people believing the world is flat.) Once you can convince people that one group of people has this essential difference, or motivation, or intent, that idea becomes a cultural talisman in its own right, sewing disharmony, distrust and leading to treating people differently just because. Those people then have to not only fight for equal treatment, they have to fight it uphill against the idea that caused them to be treated unequally in the first place.
That's not to say you make certain ideas illegal, but just like an economic market, complete lack of regulation does not work. Or it works well for some people but not for others. In the marketplace of ideas, just as in a financial one, power concentrates among those who already have power. Whether that's a willing audience, a platform, or just the means to tap into our ever present human fallibility for falsities to warp into a neat, but flawed idea that you can indoctrinate the less careful to believe.
At some point you need to draw a line and say "ok, we start from certain basic premises of equality" and go from there. Now in the UK we've typically relied on good old soft rules about "what's done" to say and what's just not cricket. Even our obscenity laws are based around what a "reasonable person" would be offended by. In the US you were way ahead in thinking when you "declared these truths to be self evident: that all men were created equal". Imagine that! A self evident truth. A truth that required no further discussion because in and of itself it was evidence of how true it was. But you skip forward a few decades and see how it panned out, and you know I think it's fair to say you gave it a good go but that self evident truth just needs a little help there so that all people can enjoy the equality of life, liberty, all the good stuff.
Opinion seems divided on where that line is. But saying that things that fundamentally and directly seek to undermine the self evident thesis of equality not just interpersonally, but throughout society, seems a pretty small concession to the practicalities of ensuring the most freedom for the most people, even if it means that you have to take it on the chin and pull back from theoretically pure notions of freedom.
We'd probably all like to be totally free on some level. To live without the need for law. But people will be people, and that's why we can't habe nice things. (And that reply works for the gun control argument as well as this one.)
Just my 2c and change and I didn't mention left or right once