General Discussion

As Klaralven pointed out upthread, Taiwan's semiconductor production is vital to the world economy, not to mention national security. That production capacity can't be allowed to fall under the control of mainland China. The world grinds to a halt without those chips, and the shortage is already problematic without it turning into a way for China to strangle the rest of the world.

On the flipside, while Ukraine isn't a member of NATO, they're the next best thing. If the Russians move in, failing to respond is basically throwing open the door to Putin's aspiration to resurrect the Soviet Union. Eastern Europe and the Baltic States, many of which are members of NATO these days, are watching closely, as is the rest of the world. Apart from geopolitical and economic concerns, it's a credibility issue.

As a practical matter, defending both is feasible. It'd certainly get ugly, but there's a reason we pour so much money into our military. A global scenario like this is one of those reasons. If nukes weren't a factor in the equation, Russia's military is nothing to write home about based on what I've seen. China can't project force the way we can, either. Cyberwarfare is, of course, a concern with both nations, but if things got wildly out of hand, they'd come out of the scrap in worse shape than we would.

Hopefully that worst-case scenario remains a mere intellectual discussion rather than a real shooting war.