Dan Ives, an analyst and longtime fan of Tesla, was scolded by Elon Musk on Tuesday after posting three steps he said the company’s board should take.

Mr. Musk’s involvement in politics and his financial support for the president’s campaign were once seen by investors as a benefit to Tesla, fueling a steep rise in company shares after the election last year. That association has now turned into a liability. Tesla shares are down 40 percent from their peak in December.