If they really were for free speech, they would realize that allowing both sides of opinion is really what free speech is all about.

Completely wrong. You're obviously way too entrenched in one-/two-party political systems like Singapore and US where everything is antagonistic, us vs them, PAP vs opposition, right vs left, Dems vs Reps, east vs west. If one side says something it doesn't mean the other side can say anything they want without consequence. Free speech doesn't protect or care about sides. If it did it would be inherently political and biased to the side in power.

Free speech is also not the freedom to say literally anything. Any democracy, east or west, has a range of things not covered by free speech. Even in the "freest" countries you can still be censored or face a range of other punishments if you cause harm, infringe on other's rights, disturb public order etc with your speech.

In this case, publishing lies about Uighur concentration camps that everyone else knows is happening could be considered to be causing harm, in the same way that some countries consider Holocaust denial to be causing harm, and thus deserving of censorship or other punishment by law. What public good could there possibly be in allowing such lies? Unless of course you have business with China.