Before state intervention or witchhunting should tread upon people's speech, maybe we need to ask what is changing that so much militancy got tolerated. And there's an element to how parties are being run
Perhaps a centralized party around a cult of personality has the advantage that the leader can sway his people away from violence. Its been taken axiomatically that dictators lead their people to violence, because we saw so much of it in the 20th century and engrained it into the public consciousness. That's also perhaps a super long term recency bias, we've had thousands of years of rules, some violent, some benevolent. With an authoritarian leader, all your eggs are in that one basket.
Right now we're seeing a proliferation of militancy and violence from the US (and global) left-wing. Yet no charismatic rulers are emerging, the closest thing to someone getting wider support is a fossilized bernie sanders. There is no Kingfish, no MLK, no Lenin or Marx. Its a rudderless movement, and yet its descending into worse and worse violence. Now contrast MAGA america. We saw bubbling strands of militancy and extremism and some sporadic violence from the far-right, we had the Unite the Right rally, magabomber. But beyond individual actors, it was a whole undercurrent of the Qanon nutcases who threatened to boil over into violence. But who tamped them down, who suppressed them? It was Donald Trump, the same guy who riled them up in the first place. Trump is the one who told people to go home and be peaceful, he's the one saying his movement is exclusionary to extremists. He's the one who decisively cut ties with neo-nazis and white nationalists. He drew his hard lines and forced the party to accept them.
Democrats don't have any of that right now. The far-left is a white hot shrieking ball of rage with nobody to keep it under any kind of control. They hate the democratic leadership, they hate each other. There's nobody shaping the progressive movement and gatekeeping to remove antifa, communists, islamists, eco-terrorists, anti-natalists, etc. The few democrats who engage with them willingly share a stage with militant radicals. If Bernie Sanders said the left should kick antifa out of the party, they'd call him an old white man, label him a colonizer and post his home address for assassins.