I think the conspiracy theorist label is associated with common patterns (believing in a cover up in cases where there's no incentive / the cover up would be more expensive than the crime / the evidence would be impossible to cover up, etc) but in this case these patterns don't apply.
The lab leak theory was extremely plausible even assuming no secret conspiracy at all. Lab leaks do happen, that lab did do gain of function research, the State did shut down investigations, etc.
You might be surprised how many things labeled conspiracy theories have strong evidence, incentives, etc. but get scoffed at as kooky impossibilities nonetheless - like the lab leak theory.
Not just main stream media. Your average javascript programmer engaged in the same antics whenever policies regarding covid were questioned.
These censorship policies wouldn't be nearly as widespread if they weren't popular among the middle of the bellcurve "I can write javascript therefore I must be very smart" type people
The major reason for that is that many were doing this in language that was generally considered racist and/or mixed in some other weird stuff like how COVID lockdowns were like the Jewish persecution, rants about masking, or that type of stuff. I'm not saying everyone did that, but there was a huge overlap.
There was a huge overlap because within a month it became completely taboo for anyone who cared about not being seen as an alt-right activist to say anything about it. Even freaking Jon Stewart got caught in the instant-cancellation blast [0].
A major problem with our world today is that anything that the alt right supports instantly becomes taboo for the rest of us. People are more concerned with distancing themselves from the alt right than they are with finding and supporting the truth—and that goes for just about anything, not just COVID.
99% of the time there isn't a good reason to censor things, that doesn't stop it from happening constantly though. Especially in China where censorship of anything with bad publicity for the country or government or people is the default stance.