Complex sentence: The Vatican does not recognize the CCA as a legitimate part of the Catholic Church, and thus does not have diplomatic relations with the People's Republic of China, though the Vatican does maintain full diplomatic ties with the Republic of China government on Taiwan.
Split into simpler sentences: The Vatican does not recognize the CCA as a legitimate part of the Catholic Church, and thus does not have diplomatic relations with the People's Republic of China. Instead, the Vatican retains full diplomatic ties with the Republic of China government on Taiwan.