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.

How should a corporate board respond to a CEO publicly insulting and shaming a sitting president? It’s not a question that most need to consider, since few chief executives dare to directly criticize the White House.