I can only think of one example where censorship should be used and that is hate groups. Hate Groups (Westboro Baptists, NeoNazi Groups) use their free speech to threaten other peaceful subgroups into being silent or use their free speech to incite violence as way of wiping the other subgroups out of existence. On the other end of the spectrum are Authoritarian governments who prevent certain ideas from being heard because it isn't in agreement with their political ideologies. That's extreme and counter productive to fostering cultural growth.
Most of the displays of free speech that I have seen are uncomfortable to some people, but the speaker usually just wants to be heard. Their goal is to voice their opinion and maybe have a few of their listeners give their words some thought. The speaker cannot force people to listen to them if they don't want to and the listener shouldn't prevent them from being heard if they aren't being disruptive in any obnoxious kind of way.
Youtube has been going overboard with demonetizing any content creators they deem "problematic." I have a few subscribed channels who create content based around pocket knives and medieval weaponry. The pocket knife channels always teach their viewers "this is a tool, not a weapon" and instruct safe handling of the knives while the sword channels demonstrate proper handling, safety and direct the audience on where to go for becoming trained in proper handling. Neither of them promote violent usage of the swords or knives in question (pocket knives are crappy weapons anyway) and yet youtube finds them problematic and as a way of getting them to leave, they have forbidden them from getting funded. This is problematic because these content creators are part of the solution to weapon violence and silencing them is counter-intuitive. It should be taught that guns and knives do have a purpose as a tool and shouldn't be used as a weapon. Promoting ignorance isn't an effective way of combating unwanted behaviors. You need to promote proper behaviors if you want to change the bad actors in the situation.
Video games are a gray area. I grew up with Modern Warfare lobbies where people would say the nastiest things to one another in the spirit of competitiveness and then I moved on from that to League of Legends where people would type out the nastiest things to one another, again in the spirit of competitiveness. Personally, I never engaged in it. Its one thing to say horrible things, its another to act on it. 10+ years ago it was just words, Swatting wasn't a thing back then, people didn't dox each other, any threats that were made went unfulfilled. Now people act on those threats and those threats need to be taken seriously. Too many psychopaths are ruining it for the majority of the people out there. Censorship really doesn't solve the issue though. Preventing them from saying n***** will just make them use a different slang word to incite their target into getting angry. I don't feel that its effective at culling the root of the problem.
I don't know search engine censorship very well at all. The only example I know of is when google got exposed at repressing non-google affiliated results from showing up in their search engine. I guess its a way of limiting exposure to smaller/lesser known sources, which is bad as it limits progress and growth. They have since fixed it though. Are there other forms that my tired brain is overlooking at the moment?