Since taking over Twitter, Elon Musk has shown a willingness, and sometimes a relish, to pick public fights with an array of targets, including advertisers, tech giants, employees and more. But over the weekend, Musk publicly attacked two figures, Dr. Anthony Fauci and Yoel Roth, Twitter’s former head of trust and safety, in ways that may resonate with far-right audiences and gin up user engagement — but are likely to deter wary advertisers from flocking back to the social network anytime soon. “My pronouns are Prosecute/Fauci,” Musk tweeted on Sunday, scoring points with both critics of the use of nonbinary...