But your belief is already logically inconsistent unless you are saying we should allow porn, animal cruelty, or ISIS propaganda on YouTube (the last one is very clearly suppression of a political opinion, and abhorrent one, but nonetheless).

This is the issue, if you are saying YouTube should allow all content then you need to be consistent and allow all content. If not you really just disagree on what content should be censored, but then you can't make this out to be a censorship vs free speech debate, because you agree on censorship, just not on what gets censored.