Why many in China support Beijing's policies in Xinjiang and Hong Kong

Over an uncountable number of official statements and state media news reports, Beijing has described both Uyghurs and the demonstrators in Hong Kong as "separatists", who are seeking to "undermine China's sovereignty". This has created a huge stir in mainland China, where people take the subject of the country's sovereignty very seriously. Many in China support human rights and democracy, however support for Beijing's often contradictory actions remains vast — so why is that the case?