Google's reason for supporting net neutrality has nothing to do with free speech, obviously. But loss of net neutrality means not just charging more for YouTube. It also means censorship because it really is very easy to censor content once you start discriminating by packet. Of course those against net neutrality will deny this, but they are wrong. Without net neutrality, ISPs can choose what content they want to deliver whether by content type or by content political correctness.
I should add that the whole arguments that ISPs are being forced to deliver high volume content for free is just bullshit. If an ISP wants to limit total content delivered to a home per month or whatever, they can do this now. This does not violate net neutrality.