The relations between Taiwan and the US have nothing to do with "democracy". First it was about anti-communism, when the Chinese government fled there and the mainland was taken over by the communists. Now it is about anti-communism and "China containment". The fact that Taiwan transitioned to democracy in the 1980s is just convenient to feed the public that this is indeed about "democracy", "freedom", the usual.

As a historical point, the US never had a problem with Taiwan being handed back to China at the end of WWII, since it is what happened. Again, this is all just a tool against the communists and then against China's increasing power as a whole.