Imagine the government decided that you go to prison for speaking against vaccines. That would be a mistake. This is the same kind of mistake, but on a smaller scale.
Imagine a straw man argument that has nothing to do with the current situation.
Better yet, imagine if the government told you that you must post a sign in your front yard that says “vaccines are good” or “vaccines are bad”. That’s a much more relevant analogy here.
Your right to not be prosecuted by the government for what you say is protected by the first amendment. YouTube’s right is similarly protected: they can say or not say what they want on their website without criminal consequences. So which is it, do you want the government to curtail YT’s free speech or not?
I am for liberty. I don't like when governments censor their citizens and I don't like when corporations censor their users or customers. There is no contradiction. The fact that google and co can censor others is just thanks to the government being liberal and allowing action that goes against this value. This is similar to the paradox of tolerance except for liberty: "do we allow free expression for those who use it to restrict others?". And I say we do, but I don't pretend to be happy when they do.
The contradiction is that you are saying the government can censor Google, just not you. So in other words you want to give the government the ability to tell Google “put this on your home page” for any value of “this”.
The only way to prevent a corporation from exercising their right to free speech is to have the government interfere. So the part where you said you don’t like Google censoring people is where you said you want the government to censor Google.