To be honest I don't think China cares all that much either because they're used to the US Navy sailing about as a reminder of our treaties with various other SE Asian countries. They're veen assertive about their territorial claims with the nine-dash line, the building of artificial islands (reportedly now weaponized), and rejecting the decision of the international maritime court recently. Overall I'd characterize relations between the Chinese government and the Obama administration as cool but respectful.
I don't know what's happening with the incoming administration and don't want to make a political argument here, but I do think that publicizing the fact of the conversation between Trump and the Taiwanese President, along with the public questioning of the One China policy, probably seems like a huge loss of face for Beijing. China doesn't mind the US having relations, even friendship, with Taiwan - through private channels. Public recognition of the Taiwanese government as a sovereign entity by the US is insulting though - much as if Premier Xi in China started having friendly chats with the governor of Hawai'i or Alaska while publicly pouring scorn on DC.
Edit: great username btw