I have some unprofessional sociological suspicions, so I will lay them out as assertions with this caveat serving as the blanket qualifier.
First, some observations:
1. Research has found that the probability of conspiratorial thinking is quadratic with respect to political extremism in either direction.
2. Dangerous political movements are predicated on an "us v. them" mentality, almost by definition of dangerous. What makes a group dangerous is precisely the fact that they are willing to harm people in concrete ways, and willingness to harm requires a targeted "them".
3. Distributed censorship and other forms of persecution are actually conspiracies with an inherent "us" and "them." The more groups (media companies, government, etc) censor similar ideas in similar ways for similar reasons, the more apt appears the description "they conspired against those ideas."
Therefore: the problem with censorship is that it makes the conspiracy theorists right. Censorship is also an acknowledgement that the censor and censored are in fact different and opposing groups. No longer can the censor say "come on guys, we're all on the same team here," they have ceded that high ground.
Both of these effects can actually help extremist groups attract new people. As they say Plures efficimur, quitiens metimur a vobis: semen est sanguis Christianorum: the blood of the martyrs is the seed of the Church.
HOWEVER
All of this analysis is a kind of "perfect sphere on a friction-less plane" view of the market of ideas. We must not fall into the trap of thinking that if we removed all censorship, the market of ideas would be efficient. If censorship is an effort to artificially devalue some ideas, there is also the countervailing force of amplification which artificially inflates.
The problem is that money has always (and technology has recently) enabled people to distort the market of ideas through amplification. There are actually bad actors (e.g. Russia) who actively amplify ideas beneficial to their interests by putting engineered talking points into fake social media accounts.
I do not believe it is possible to fight such a strategy on the same terms. Amplifying contrary ideas simply increases polarization. Attempting to re-level the playing field via censorship has the problems I listed earlier.