Free speech and democracy do not tell people what to believe. These give people a voice at higher levels of government. It is a way to avoid conflict and enable everyone to contribute to the progress of society.
Government officials in China are not chosen by the people. The "People's" republic is a farce. Those who disagree with policy are expelled or imprisoned. BLM may be ignored and discounted by some, but they have a voice and can effect change. Tibetans, people of Xianjiang, Falun Gong, and countless other would-be activists have no such path in China.
Many American politicians have been quite receptive to the BLM movement.
China, on the other hand, regularly imprisons protesters indefinitely.