On Oct. 12, Virgin Group founder Richard Branson announced he was pulling out of talks on a $1 billion deal with Saudi Arabia over the killing of a Washington Post columnist. State involvement in the killing, “if proved true, would clearly change the ability of any of us in the West to do business with the Saudi government,” Mr. Branson said.

Days later in a text message, Mr. Branson counseled the Saudi crown prince, Mohammed bin Salman, to release female activists his country had imprisoned.

“If...