A key difference is that the governments of the British colonies in North America were officially installed by, and reported to, Britain.

cf. the Taiwanese government, the KMT, which at one point controlled the mainland, but was pushed into exile on Taiwan by the communists. The existence of a free Taiwan threatens the legitimacy of the communist government on the mainland: the PRC, like most propaganda-fueled authoritarian regimes, does not like anything that suggests there's an alternative to their system.