Does the United States rule Taiwan?

Obviously not, de facto. Taiwan is ruled by the people of Taiwan, via their elected government. The Beijing dictatorship is working hard but patiently to destroy Taiwan's sovereignty, and to bring Taiwan under the rule of the unelected kleptocracy which currently oppresses China, Tibet, and the Uighers.

But as a pure matter of international law, who is the sovereign of Taiwan? Perhaps the United States military government. China exercised sovereignty over part of Taiwan beginning in the 17th century, and asserted (but did not exercise) sovereignty over the whole island for fewer than 20 years in the 19th century. In the late 19th century, China transferred Taiwan to Japan, which ruled Taiwan until 1945. The Japanese forces on Taiwan surrendered to the American military, and so by the established laws of war, the United States became the occupying power. In the 1954 San Francisco Peace Treaty, Japan renounced all claim to Taiwan, but the treaty did not otherwise specify the status of Taiwan, and so the U.S. remained in charge, de jure if not de facto, as it does to this day. So goes an argument you can find in the Harvard Asia Quarterly, among other places.

So some Taiwanese filed a case in which they asked the the U.S. Department of State be ordered to issue them U.S. passports; they argued that legally speaking, they are "U.S. nationals" but not U.S. citizens. On Tuesday, the D.C. Circuit Court of Appeals issued an opinion stating that the plaintiffs might be correct as a matter of law, but that the the Political Question doctrine prevented the D.C. Circuit from deciding the issue.

I think that the D.C. Circuit's decision on the Political Question doctrine was correct. And I realize that a U.S. affirmation of sovereignty over Taiwan would very likely lead to a war with China, and so such an affirmation should not be made without full debate in the political branches of government, including a vote of Congress. Nevertheless, the people of Taiwan are about the most pro-American, pro-democracy, and well-educated group as can be found anywhere on the planet. Yes, Ireland and Israel would be close contenders, but the U.S. has no legal claim to sovereignty over either of those nations. It would be a better world if Taiwan's politicians were (like the politicians in American Samoa) debating the terms of their legal relationship with the United States, rather than worrying about how to avoid being engulfed by the tyrants of Beijing, and turned into an island version of Tibet's hell on earth.