The US still retains the option of a nuclear first strike. China, on the other hand, does not.
If incoming medium-range ballistic missiles are inbound for a ship, then I'm pretty sure the US experts can already figure out that it's a DF-21, not some nuclear-tipped ICBM. A nuclear first strike would involve hundreds of missiles simultaneously with intercontinental ballistic missiles, and the target would be the mainland US. A DF-21D strike, on the other hand, involves a single medium-range missile and the target is a military ship.
Even if they view it as a nuclear attack, why risk nuclear war for an incoming missile that might not even be nuclear? The risks are too high to gamble.