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.
It is possible to distinguish between censorship and spam filtering. In the case of censorship, the speaker wants to say something and the listener wants to hear it and the censor prevents this. In the case of spam filtering, the spammer wants to say something and the listener doesn't want to hear it and voluntarily requests that a third party filter it out, with the option to individually disable this filtering.
Now, someone could implement censorship and call it a spam filter, e.g. it filters spam and also disfavored facts and people leave it on because there is only a single on/off toggle and they don't want to be deluged with spam. But what this implies is that a "spam filter" with uncorrectable "false positives" is equivalent to censorship.