Do you in good consciousness support the U.S. government? I'm asking because the government doesn't recognize Taiwan as an independent country and kicked Taiwan out of the United Nations in 1971.
What kind of question is that? No citizen supports all the actions of their government. Government options are a lot more limited than employment options.
It's true that the US government officially recognizes the Beijing government as the legitimate Chinese government and doesn't recognize Taiwan.
OTOH, the US has a security partnership with Taiwan. See https://www.brookings.edu/research/the-united-states-securit... for details of this unique relationship.