The West only cares about free speech in a procedural way, not in any sort of substantive way. Much like how it cares about democracy in only the procedural sense of people being able to vote (and even then inconsistently), but doesn't at all care about whether the options people are voting for will do anything to act in the interests of the people.

In the same way, the West cares that the government is not directly censoring you, but goes out of its way to ensure that media and internet companies are controlled by those who will censor on the government's behalf.

In this way, the Western belief in spreading "freedom and democracy" is essentially a new interpretation of the previous project of spreading Christianity - a purely surface level of veneer of moral good used to browbeat others, while in no way following the actual teachings of everyone's favorite brown Socialist carpenter.