If your problem as a society is the spread of extremist content and ideology (in parts because social media algorithms reward everything that provokes reactions), than "doing things" to avoid specifically extremist content linked to terrorists might not be a bad start?

Isn't this the way the US government treats islamist terrorist propaganda too? I am not sure why we should treat rightwing terrorists different. Both are inhumane, cruel and undemocratic ideologies, that would end free speech as soon as they get in power.

Note that this is meant to target right wing extremism, not right wing ideas per se. I am all open for discussion, but when people start promoting violence, genocide and hate, maybe a society is better off not protecting them unconditionally.

Free speech is also a cultural issue, e.g. in Europe you could shock some people with explicit violence, while nobody cares about exposed female nipples. In the US it is exactly the other way round – they are extremely open to violence, while in other areas free speech doesn't seem to count as much.