This isn't true. Democrats were heavily pushing the PRESS act for example, which would expand speech protections for journalist and reporters. This was tanked by Republicans.
> They see nothing wrong when someone is put in jail for "causing gross offense" on Twitter
You keep repeating this but not providing any sort of evidence to it. Again, you seem to be talking about the boogeyman that Republican talking heads have created instead of pointing at any actual policy. I would advise you go outside and talk to actual people.
> As for the rest of Europe, just look at the knee-jerk hysterical, pearl-clutching response to Vice President JD Vance's recent speech about the EU and its values, and how much of that response was coming from the left.
Most Republicans talking about free-speech are hypocrites and liars including the President, Vice President, and their first buddy. I imagine that has more to do with the reaction than anything else. They don't walk the walk but love to talk the talk.
Intolerance isn't just "causing offence", it is the creation of an environment which is threatening. If ou get enough veiled anonymous threats against your life, health and family then you might well withdraw from public life. And then, what value does "free speech" have for you?
But, you say, you aren't talking about threats, just about "offence". But offensive speech begets threats. If Mr Rabblerouse publicly calls Jenny Good out as a dangerous degenerate, some of his followers will, quite predictably, follow his lead and start to make actual threats. Some might go further and carry out those threats. Even if they do not, Ms Good is going to have a perfectly reasonable fear that they might.
You say that Mr Rabblerouse is merely stating a legitmate opinion, that he has a right to be offensive, and that the Ms Good is equally free to say unpleasant things about him. But that is just deliberately ignoring the power inequality. Ms Good has no mob who will take the hint to hate on Mr Rabblerouse, no power to put him in fear. But he does have the power to do it to her, on a whim, answerable to nobody. And when people see that, and see how easily he can put Ms Good in fear and misery, they will think twice about their own speech.
And this is the point. Hate speech is not merely unpleasant and worthless, it actively suppresses the speech of other people. US jurisprudence makes much of "chilling effects" of government action on speech, and with good reason. But it is not just the government that can chill speech. Mr Rabblerouse can chill the speech of others against himself very effectively. So the only way to ensure freedom of speech, paradoxically, is to ban speech that incites hatred.