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.

When President Donald Trump won the election in November, investors viewed Tesla Inc. as one of the biggest winners. That bet now seems to be on shaky ground after investors watched the once formidable alliance dissolve in real time.