You used the words "moral obligation" in a serious discussion. Thats what Im calling you out for.
The U.S.A and Taiwan did have a defence treaty that ended in 1979 called the 'Sino American Mutual Defence Treaty'. This was replaced by the 'Taiwan Relations Act' from 1979 - current.
Section of Taiwan relation act:
"Military provisions[edit]
The Taiwan Relations Act potentially requires the U.S. to intervene militarily if the PRC attacks or invades Taiwan. The act states that "the United States will make available to Taiwan such defense articles and defense services in such quantity as may be necessary to enable Taiwan to maintain a sufficient self-defense capabilities". However, the decision about the nature and quantity of defense services that America will provide to Taiwan is to be determined by the President and Congress. America's policy has been called "strategic ambiguity" and it is designed to dissuade Taiwan from a unilateral declaration of independence, and to dissuade the PRC from unilaterally unifying Taiwan with the PRC.
The act further stipulates that the United States will "consider any effort to determine the future of Taiwan by other than peaceful means, including by boycotts or embargoes, a threat to the peace and security of the Western Pacific area and of grave concern to the United States".
This act also requires the United States "to provide Taiwan with arms of a defensive character", and "to maintain the capacity of the United States to resist any resort to force or other forms of coercion that would jeopardize the security, or the social or economic system, of the people on Taiwan." Successive U.S. administrations have sold arms to Taiwan in compliance with the Taiwan Relations Act despite demands from the PRC that the U.S. follow the legally non-binding Three Joint Communiques and the U.S. government's proclaimed One-China policy (which differs from the PRC's One-China Principle)."
Its deliberately ambiguous and open ended in regards to defending Taiwan, like a lawyer covering his clients ***.
Let me tell you this though - The USA government have a "moral obligation" not to get their citizens involved in a war with a country 1000 times stronger than the ragged towel wearing militants your military is accustomed to fighting.