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.

Though their war of words on social media has slowed, the world’s richest man and the U.S. president isn’t over yet as Trump vows to sell his Tesla.