Russ Hudson was not supposed to be in Scott Colom’s protein ad. Mr. Hudson, 35, had known the district attorney for about a decade before Mr. Colom became the Democratic candidate for Senate in Mississippi. But it was Mr. Hudson’s father who was initially cast in the campaign ad mocking a suggestion from Senator Cindy Hyde-Smith, the Republican incumbent, that Mississippi residents pick another type of protein to avoid rising beef prices. When the elder Mr. Hudson balked at a script that would require him to utter profanity on camera, his son volunteered. In a short-sleeved button down shirt, he...