Bristol Smith, a manager at a McDonald’s in Maryville, Tenn., came across Vivek Ramaswamy’s name this spring, shortly after Mr. Ramaswamy, an entrepreneur, announced he was running for president. Mr. Smith was intrigued. He liked the way Mr. Ramaswamy “stands up against the wokeness” and his plan to send the military to the southern border to combat drug cartels. He respected Mr. Ramaswamy’s acumen as a businessman worth hundreds of millions of dollars.