Elon Musk’s bitter falling-out with President Trump could be costly for Tesla. As long as he is persona non grata in the Trump administration, Mr. Musk, the chief executive of Tesla, will struggle to persuade Republicans not to gut climate policies worth billions of dollars to the electric car and battery company.

Traders dumped Tesla after Musk quickly responded to Trump's criticism with social media posts that stepped up criticism of the president's tax bill.