That's the problem with the discussion on free speech and censorship. They almost always are categorized incorrectly from the outset. Free speech doesn't exist on a media forum operated by a private business, be it YouTube or Twitter. The site owners are completely within their right to block whatever content they choose to. The censorship discussion is equally mischaracterized, often purposefully and maliciously to spread disinformation, as in Beamer's Fox News example. That isn't censorship; that's protection of the public from purposeful misinformation that can cause actual, severe harm.
Often the argument gets made that by choosing what information to allow versus what to stifle, an organization is dictating what can be accepted as truth. That is indeed a concern and could lead to some Orwellian situations if abused. By all means, fight against that. But when you do, have some actual verifiable proof of what you are claiming. You want to claim that an election was stolen? Well for a charge that serious you had better have actual verifiable evidence that goes way beyond - I mean WAY beyond - what has been presented thus far. COVID and the January 6th insurrection prove beyond a shadow of doubt the extreme dangers of what can happen when the public is knowingly lied to under the guise of free speech.
“The greatness of a nation and its moral progress can be judged by the way its animals are treated.”
- Mahatma Gandhi