Almost all Americans can agree on freedom of speech.
Freedom of speech is what the US Constitution guarantees. It says the government cannot limit people's ability to speak their mind, and cannot punish people for speaking their mind. Note that it says nothing about what private entities can do, especially on platforms they own and operate.
"Free speech", as exercised nowadays (mostly) by conservatives who complain about being "silenced", is the (in my opinion ridiculous) idea that one should be able to say anything they want without any consequences whatsoever, and that they are entitled to any platform they choose to spread that message. These are the same people who advocate for a "marketplace of ideas", but get bent out of shape when that marketplace reacts negatively to their opinions.
In my opinion, we need to rid ourselves of the idea that all ideas are equally valid and deserve equal amounts of airtime and consideration. Furthermore, it is okay to completely dismiss certain ideas on their total lack of merit, and furthermore take (private) action to prevent their spread. For example if I post on this site that "all people of <insert ethnicity> need to be exterminated" it would be completely okay for others here to downvote/flag my post (i.e. "censorship") and for HN to ban me (i.e. "de-platforming").
Conservatives tried this too, recruiting the aid of the government to fight against obscenity, Communism, etc. And they lost that battle in the end.
(I assume you follow FIRE, and know that this problem isn't contained to the "speech is violence" people; there are numerous right-wing attempts at suppression on campus as well.)
As to your second point, FIRE tends to advocate for free speech on campus generally, including private schools. A lot of the right-wing attempts at suppressing speech happen at places like private religious schools (Duquensque and Georgetown are two top posts in the FIRE website). I tend to stop short of that—I think private schools are free to restrict speech in ways public schools are not. But, as I said in my post, attempts to suppress speech have historically been a right wing phenomenon.
What would you call this event? The genocide of ideas (by the righteous)?
Who decides which ideas are invalid or lack merit? Is there a social credit system to value / devalue those with ideas and prevent them from transmitting them?
At what point does it extend from the online world into every day life?
What happens to those people when they can't express themselves online or in real life?
Do you see where I'm going with this?