This isn't a free speech issue, no one is suggesting that this content be removed from the internet.
The issue is that sites like YouTube don't just provide content, they also promote it by showing people recommendations. No one is suggesting that climate change deniers should be prohibited from expressing their views, just that YouTube should not promote it.
Take a more extreme issue: flat-earthers. Someone who believes the earth is flat should definitely be able to say so, but it's not a good idea for YouTube to actively promote that viewpoint. It's also just as bad for YouTube to present the issue purely as flat-earthers versus non-flat-earthers, as it suggests there is some sort of balance between the viewpoints.
To the extent that YouTube is promoting content, they should do within some bounds of reasonable consensus. If they refuse to police their recommendations, they aren't improving free speech, they are just destroying the existing mechanisms of consensus.