DETROIT—If President Trump’s trade war has a physical battleground, it is Michigan, where companies and workers are already feeling the beginning of an onslaught that could blow a hole in the state’s economy. Nearly 20% of the economy is tied to the auto industry, which has become increasingly dependent on parts and vehicles from Canada, Mexico and China—imports Trump hit with steep tariffs in recent weeks. This trade has grown so large that Michigan ranks fifth in the nation by the size of its imports and exports, even though its total economy ranks 14th. Detroit’s automotive executives have shifted into...