China in its current totalitarian form needs an "Enemy" to survive, without it, it has to deal with difficult internal questions which will force it to adapt and change - and this what scares them.
Totalitarian governments rely on distraction and misdirection of the populace in order to survive. Without it to use as ammunition to unify the people against a commonly perceived "enemy", the very nature of its limiting rule forces the populace to start questions to try and improve their own condition. Questions like "freedom" and "censorship". Totalitarian governments are not equipped to satisfy difficult questions like this and will either adapt or crumble.
Thus the best way "oppose a government that is the sworn enemy of values you regard as precious" is to allow it to face its internal discord without giving it the "enemy" it so desperately needs as ammunition to use against you.
EDIT: There are many comments that I think are misguided attacking this concept, here is rebuttal to them:
Proposition: If China wants to make the west an enemy, it will do so with or without us by the total control it has over its populace.
Rebuttal: So the best counter plan is to help them in doing so?
Proposition: So the solution is don't speak out about real issues because you don't want to piss off Chinese citizens and make them think you are the enemy?
Rebuttal: Obviously not, but rhetoric implying war or xenophobia is hardly the answer either.
Proposition:Most totalitarian governments fail on the battlefield. Think of Genghis Khan, Napoleon, the empires that fell during WW1, or the Axis powers in WW2.
Rebuttal: Just because totalitarian regimes have fallen on the battlefield before, does not mean they will do so in the future. Not only is this proposition utterly foolish and dangerous but its not even remotely true in the nuclear age.
Proposition: Even if you watch or read the heavily controlled Chinese media, it's never about fighting anyone or pointing the finger at anyone.
Rebuttal: This is almost categorically untrue and uninformed. In fact, in times of political tension anti-west and anti-Japanese sentiment in the government controlled media is used almost without fail. No protests are allowed, but anti-west and anti-japanese protests are manufactured by the state.
Proposition:Should we allow economic coercion and suppression of political speech in the US by a state power? Can we not speak out in favor of those protesting in Hong Kong that were promised 50 years of "one country, two systems"?
Rebuttal: Of course NOT! But we should act on the defensive, and prudently, with our own best interests in mind.
Proposition:This theory has proved wrong. China has been welcomed into the WTO over the last 20-30 years and it has not reformed. It is now extending it's economic superpower into political and cultural power. It's not about making an enemy, it's about limiting this unwanted influence.
Rebuttal: To say the theory has proved wrong is premature, China took advantage of one sided trade agreements that created a competitive advantage for itself, subsidized by us. Limitations of its political and cultural power should be in the form of leveling out this competitive economic playing field, and not escalation into xenophobia or coercion.