Final answer:
The statement that Beijing continued to object to the U.S.'s non-official relationship with Taiwan even after diplomatic ties were severed is true. The U.S. has continued informal relations with Taiwan, including trade and the establishment of de facto embassies, such as the American Institute in Taiwan, resulting in diplomatic tensions with China.
Step-by-step explanation:
The main answer to whether Beijing continued to strongly object to the fact that the U.S. maintained a non-official relationship with Taiwan, after Washington broke diplomatic relations with Taiwan, is True. The explanation for this is that Mainland China, or the People's Republic of China (PRC), has consistently insisted that diplomatic relations with the PRC require the non-recognition of Taiwan (the Republic of China, or ROC). Despite the United States officially breaking off diplomatic relations with Taiwan in 1979 to establish formal relations with the PRC, the U.S. continued to engage with Taiwan through non-official means, such as trade and the establishment of de facto embassies like the American Institute in Taiwan.In response to continued U.S. relations with Taiwan, including arms sales, China has acted defensively, for example, by denying port access to U.S. ships at various times. The ongoing struggle over Taiwan's status—whether it is an independent country or a part of mainland China—continues to cause friction between the U.S., China, and Taiwan. These historical dynamics and policies, such as the "One China" policy, underscore the diplomatic tightrope the United States walks in maintaining a strong yet unofficial relationship with Taiwan while pursuing formal relations with China.