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.

President Donald Trump and billionaire Elon Musk are showing no signs of reconciling on Friday, but Republicans are increasingly urging them to settle their dispute.

For all the insults that Mr. Musk and Mr. Trump traded on Thursday, don’t be surprised if they make up again days from now. In the meantime, they both benefit.