No individual or private party can "force" anything off the internet unless that person has the force of law behind its otherwise private action.

The communist system of law is undergirded by a philosophy that assumes humankind can be reshaped and reorganized to achieve a collective goal for society that ultimately is ushered in by force. That is why freedom is lacking in such societies. One can be completely cynical about this and point to the way such societies have historically degenerated into slave camps but there is actually a form of "idealism" at work here, to wit, a view of humanity that says we can be molded from scratch to conform to a model of state government that enforces state ownership, state education, and state dictates as the central components of life, presumably to the betterment of society. Inexorably linked with this philosophy of the state is the idea that those who are being molded and shaped toward the ultimate goal will be exposed to and accept the ideas that animate this system and will not deviate from those ideas. A collective effort requires a collective will and there is little room for diversity of ideas when everything in society is shaped and directed by a centralized authority toward a common goal. Hence, it is natural and logical for a communist government such as that found in China to suppress all ideas that conflict with the idealized view of humanity that this government is currently forcing down the throats of its citizens. Law is law, and it is backed by fines/imprisonment/executions, etc. that enable a central governmental authority to use force to realize its will. If that centralized will is aimed at the strictest control over the most minute lives of its citizens - as it typically is in a communist system - there is no room for freedom of expression or for any beliefs or ideas that deviate from the narrow range of ideas that are deemed acceptable by those controlling the instruments of force in such a society.

In contrast, the western system of government, which generally is based on the ideas of capitalism and freedom, tends to be animated by a philosophy that sees citizens as being free to follow their diverse pursuits, goals, and dreams. This system is not anarchistic - government plays a crucial role here. But it is a role where the force of law is used to set up an infrastructure of private property and private rights where human freedom can flourish (in the ideal case, it being the case that no such system has yet been implemented without even flagrant flaws in it). Law, and the force it involves, is essential to such a system. If I have an exclusive right to own and occupy my home, this means that I have the right to exclude you from it - and, if you try to trespass, or to break and enter with the intent to steal, I can invoke the force of law to sue you in a private legal action that ultimately is backed by a sheriff ready, willing, and able to enforce collection of money judgments and also by police officers who will arrest you, courts that will try you, and jailers who will incarcerate you for your transgression. Force, or the threat of force, is behind any such system and, without this, the system could not work. Yet that force is limited by the philosophy that underlies our system - to wit, that the best government is not one that can use unlimited force without restraint on its actions but rather one that is checked, balanced, and restricted by things such constitutions that set the ultimate rules and that bind and limit all governing authorities. Without this philosophy, these constitutions would be the mere pieces of paper that they amount to in communist systems. With them, the shared values of society are realized, the governmental systems are checked while still enforcing an infrastructure that supports freedom, and we realize the fruits of enjoying a comparatively free flow of ideas, beliefs, and other information, along with all the other freedoms that we take for granted.

The Disney example is one of the force of law being used to enforce private property rights - in this case, the exclusive rights Disney may have to its intellectual properties. Though IP is intangible, and constitutes what might often be called information, it is nonetheless a form of private property that is under the exclusive ownership and control of whoever owns it. And, as with other forms of private property, the law stands behind it ready to apply force to protect the rights society may value in such forms of private property. Though enforcement of such rights is by force of law, and though (at this level) our system has a shared trait with a communist system that also uses the force of law to enforce its dictates, this system of private property has nothing fundamental in common with that of a communist system - indeed, it is the very antithesis of such a system. The one promotes and protects the individual and private parties as ends in themselves by using an organized system of government designed precisely for that purpose. The other (ideally) promotes and protects the interests of individuals and private parties by using an organized system of government whose goal is to enforce mass conformity to the declared purpose of the state to reshape humanity based on a collective means of ownership.

Of course, one can take issue with whether IP constitutes a legitimate form of private property that should be backed by the force of law. The various aspects of that debate can and should be argued by the citizens of a free society. But it is not legitimate to suggest that IP takes on a bad odor simply because it shares a superficial and incidental element (that the force of law ultimately restricts an otherwise unrestricted free flow of information) with a communist system of government. A government can censor and suppress ideas in ways that stop all free debate and that ultimately can transform a free society into a tyrannical one. That is what China does. A government does not "censor" ideas and information by declaring that a private individual or entity has an exclusive right to exploit the IP it has created, even though this has the incidental effect of limiting who can use that IP as long as it remains owned by that party.

Thus, the two cases could not be more different, and the word "censor" hardly makes them identical or even similar in any material respect.