Taiwan has been independent for 70 years. Neither they nor the Chinese want to admit it, but it is plain for anyone to see.
I’m not sure its always in our interest to play along.
Especially, if we are in tough negotiations with China on a whole list of subjects including their military restiveness, I don’t know why its a good idea to preemptively surrender on every issue including giving our back to an ally. It hasn’t worked so far.
But, at the same time, they have been drawing closer together economically. The Chinese have a major-ego issue about controlling Taiwan. But, they should be patient. A war to conquer it won't do anyone any good.
In principle they are independent but I have many good friends there who do not speak of China at all on social media. Fear.