Oh yes, of course, because this approach was totally taken in those historical cases, and not totally different things that happened.
Oh wait, that isn't what happened because this approach is relatively new.
For evolution/intelligent design/young-Earth creationism, you had religious people pushing for "equal time" in school. This didn't privilege the fact-checked answer of evolution and enshrined creationism in the institution of learning, rather than having it just be something someone said on the Internet. Also crucially, the main conduit for creationism is direct transmission between believers. Even in most countries and states without creationism in their curriculum, belief in creationism hovers around 20%. Censoring creationism isn't going to be effective, and it makes sense not to give the viewpoint equal time in schools.
As for climate change, first of all, most people in the US actually do believe in climate change at this point, and belief in it being a serious problem that needs action now is the majority viewpoint as well. As for the techniques used to stall public belief in climate change and sow uncertainty for many years, they were oriented around publishing a minority of scientific papers and paying a minority of scientists for support, which could be cited as evidence against climate change (again, hijacking trusted institutions to push a narrative) to introduce uncertainty into the discussion, as well as using alternative channels of information which didn't present the majority fact-checked viewpoint at all and instead focused on the anti-reality viewpoint. This isn't the same as presenting fact-checked information prominently over misinformation that someone on the Internet is saying.
Side note: while researching current belief levels in climate change, I found out that China has been pushing that climate change is not a crisis, so belief that climate change is a problem is very low in China. It seems like the party line narrative is that the Chinese government has it under control, which is ridiculous as this is an international problem that China can't fix by themselves. This is an example of the party line being anti-reality, which can happen too.
Anyway, if the only choices were full censorship or taking no action, wouldn't the wealthy, politically motivated groups behind these issues have gone straight to using the tool of censorship? I'm sure the creationists would have loved it even more if in some states they could have removed evolution from the curriculum entirely, and the success of this measure is quite plausible. The battle over climate change also would have gotten much uglier too, with full censorship of climate change being at least attempted. This is most plausible to have succeeded in the early phases, where fossil fuel companies knew about the problem but the public didn't and even ideas like global cooling were mainstream. After all, if global cooling is the problem then you would be causing harm by cooling things further. While I'm sure this would have eventually fallen apart as the warming became more obvious, it might have made our situation today even worse. Instead, the fossil fuel industry accepted a less aggressive plan, since they were more worried about their short-to-mid term profits and a more aggressive plan would have been expensive and messy.