We arent talking RIGHTS. Can you think of life outside the scope of the law at all????? How boring can you be that the only possible conversation you have is 'but the law says'.
You can take a company to task on moral grounds, without ever having the support of law. Laws are often compromises, ideals dont compromise. We are discussing the ideal of Free Speech.
But I am also talking about moral ideas. You want to stifle Youtube's free speech, their freedom of association, their property rights. If your view is "They should have to host things they don't like," then you are saying you want to infringe on their rights. Ideals DO indeed have to compromise because with things like rights because the only way for unlimited rights to exist is for only one person to have them. If we are all going to have rights, it means that my rights and your rights will come in to conflict at some point and we'll have to compromise on that, we have to discuss where do we draw the line, how do we balance things.
The reason I'm hammering on this so hard is because this situation right here is a consequence of the right-wing libertarian ideals: The idea is that you have a right to do whatever you want with your property (some take that to the literal extreme), that you have a right to do what you want with your money, and that you don't owe others anything in terms of equal time or access or use. Ok fair enough, I don't agree with that ideal but the US in general has gone quite a bit that way (not completely, there are restrictions, but much farther than many countries). However you then have to accept this is one of the results of that. A company can do something you don't like, they can use their platform to espouse views you disagree with and shun those you do and that is just them exercising their rights. Their property, their money, their platform, their rights.
If you don't agree with that, that's fine, I don't agree with it. I think we need a more left-wing view of freedom and particularly corporate rights. But it is highly hypocritical and inconsistent to want a very laissez faire, "I can do what I like with my stuff," situation but then to not want that for others.