Freedom of speech is a fundamental human right. No ifs or buts about that.
In the same breath, it is very important to realize that your freedom of speech does not absolve you from responsibility for what you say. It does not obligate others to facilitate your speech, it does not entitle you to any platform you wish, and it does not obligate anyone to listen to you.
Similarly to the second amendment, which enshrines your right to own weapons (being the foundation of a well-regulated militia and so on) does not obligate anyone to provide you with weapons, nor the facilities to train with and maintain weapons, and it certainly doesn't require anyone to admit your onto their property if you are currently holding any weapons.
There is no legal obligation for YouTube to listen to us, but there is no reason we can't ask for less censorship. If they say no, then they are well within their rights, but we don't have to be happy about it either. Just because we can't legally force change doesn't mean we must abandon the cause. The most optimistic scenario would be if public sentiment changes enough such that YouTube feels they are being seen as unfair and it is damaging to their reputation/bottom line, perhaps we may see a change in their censorship policies. This is an ideal to strive for, and uses social/economic pressure as opposed to legal pressure. It is like your obligation to be a helpful neighbor or to be a caring friend. It's not by force of law, but people are expected to do it because it's "the right thing to do." In the same way, when you're the predominant video platform on the internet, the right thing to do is not to censor opinions you disagree with.
Sure, astroturfing and other misinformation campaigns can happen if speech is truly free, but the alternative is far worse. With free speech, if your ideas have merit then at least there is a chance they will be recognized and your audience can grow. With complete censorship, you have no chance at all. Free speech is the least bad of these two options.