Censorship, beyond what’s required by law, is doomed to fail.
So you can lose credibility two ways, one by not doing any censorship because people on the internet will be the worst if you let them. Doing too much censorship is also bad because people don't like that either. Of the big causes of censorship currently, I think of things like youtubes copyright claim process and how that is routinely used as a censorship backdoor by anyone - including the police. Sometimes its not even for any good reason and done by unthinking bots. This is banning more perfectly fine content than anything the government has done. I don't understand why there isn't more pushback against that process to punish people for frivolous claims.
Even after you start to hear about an example here & there, it still feels like an isolated and insignificant example. You as a viewer don't have any way to perceive the scale, the mass of what is being blocked and diverted and modified and bowdlerized. I mean to include all the ways creators taylor their stuff and self-censor so that it will get through, not just plain take downs.
Everyone knows it happens, but you have no way to see what that really means in it's totality. I think people would push back a lot if they could see that somehow.