Forget Apple Inc.’s smartwatch. When it comes to goods the Trump administration exempted from its latest blitz of tariffs on Chinese imports, the cases of fluorine salts and carbonate esters say more about where the U.S. is vulnerable in its reliance on Chinese supply.

The chemicals, used to make electrolytes for electric-car batteries, are among 297 dispensations sparing importers the new 10% levy. The mineral barite, which helps energy companies drill for oil and gas, and the painkiller ibuprofen—90% of which comes from...