It would be foolish to see this as a left v. right issue. This is an authoritarian vs. libertarian battle.
This sort of activity is what the government 100% shouldn't be involved in. Having a department of What is Allowed To Be Said is one of those ideas that gets tried regularly and has a terrible track record that - inevitably - ranges between a source of mild shame in hindsight to a nightmare influence on society.
There are nearly no scenarios where it is acceptable for the FBI to be in regular contact with Twitter asking for Tweets to be taken down, and if there are it should be transparent and documented - in public, in real time. It shouldn't take Elon Musk spending too much money to get details on the FBI's censorship programs (similarly it should have taken Assange-Manning-Snowden to get details on the pervasive spying).