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You say this as if China was not already preparing to do exactly this during Obama's presidency. If anything the signals Trump is sending now is defensive of Taiwan and acting to protect Taiwan from PRC aggression.
The last time the mainland seriously threatened to invade Taiwan was the mid 90's when the PRC conducted a series of missile tests in the waters around the island. This was Taiwan's version of the cuban missile crisis. Bill Clinton sent two carrier groups to the Taiwan straights in the largest American demonstration of military strength in East Asia since the Vietnam war, and enough nuclear missile boats to bomb the PRC into the stone age. The point, which got across, was although the USA would go along with whatever diplomatic One China double-speak nonsense at the UN and Olympics or whatever, the US will go to war over Taiwan. If the PRC invades Taiwan, it'll be fighting the US army, navy, and air force in what can only be described as World War 3. This was a red line never to be crossed. Officially the US agreed with the "One China" policy, but in reality the US would go to war to defend the two-China status quo. From then in '96 though Clinton's second term, and both terms of George W. Bush, Taiwan was secure & growing economically.
Then Obama signalled support for a One-China solution early in his first term. Not "yeah, yeah whatever" one-China policy status quo, but hints at full you're-on-your-own-Taiwan, let's-be-best-buddies-with-the-mainland policy. What followed over the last eight years is steady escalation on the Chinese side: artificial island expansion into the south China sea, harsher crackdowns of unrest on the mainland, direct meddling in Hong Kong electoral policy in violation of international agreements, and most recently an attempt at a diplomatic one-state solution. All this time during this escalation both the PRC and the ROC have been looking for a US response and getting basically nothing in terms of assurance of their continued support of Taiwan.
This culminated in a free-trade agreement between the ROC and PRC that was ostensibly for economic reasons, but would have set Taiwan on a Hong Kong like reunification pathway because of the unification of key financial, IT, and defence-critical industries. You can't wage war when you opponent has backdoored your entire infrastructure. Then something happened the PRC did not expect: the Sunflower Student Movement, aka "Occupy Taiwan." This massive student protest uprising had at its peak a hundred thousand people in the streets, stormed the executive and legislature, and ultimately led to the downfall of not just the free trade deal that would have crippled Taiwan, but the nationalist government as well. The anti-unification, pro-independence green party now holds power.
So where does that lead us with Trump? You comment makes it sound like Trump is not willing to defend Taiwan. But if anything his actions so far have indicated otherwise -- Trump has been very vocally anti-China (mainland). Trump is business focused and Taiwan is a strong economic ally of the USA. Trump's preference to speak to the pro-independence leaders of Taiwan before talking to China indicates support for the island nation.
China is reacting to this in a huge way, yes. Because it is a reversal of the pro-PRC Obama policy, and a probable reversion to the Bill Clinton policy of putting a red line across the Taiwan straights: go too far, and the US will not hesitate to fight in the defence of Chinese democracy.
The big unknown here isn't Trump. It's domestic Taiwanese politics. The green party is a mess and absolutely destroying the country. They're spending more time squabbling over whether they should rename monuments and change history textbooks than actually governing the country, and the party is corrupt. Furthermore, if they actually carried through on independence and established a Taiwan that is explicitly not "China", then that would negate the Clinton-era ideological justification the USA has for protecting Taiwan as Chinese-democracy-in-exile.
In my own humble but informed opinion, control over the future trajectory of Taiwan lies more with Ms. Tsai Ingwen than Mr. Donald Trump.
If he would be the usual politician that would be true. On the other hand he isn't.
He's a person who said that Japan and South Korea should not count on the US defending them but maybe develop their own nukes.
Trump builds up a bargaining position. It's not certain how much consists of bluffing and what's serious. It's not clear what he wants from China or from Taiwan.