Taiwan? Not sure. The US would definitely have to step in somehow, if China went after the Philippines.
As mentioned above, the SCS is a vital area for shipping. It’s also thought to have vast underground resources. As China starts to harvest those resources, the tension will build quickly in the region. Seeing as the Philippines have claims to parts of the SCS, China has technically already invaded them, with their recent actions. The US has made sure that the area is still open to shipping, but has done little else.
Trump is a wildcard. There’s really no telling what he would do, if either invasion occurred during his tenure as POTUS.