The film “Leave the World Behind” centers on the idea of mistrust and how easy it is for humans to lose empathy for one another when faced with a crisis. It is at once unnerving, misanthropic and bleak, and, perhaps somewhat surprisingly, it’s produced by Barack and Michelle Obama’s production company, Higher Ground. Set to become available on Netflix on Friday, it is one of three films from Higher Ground that will be released within a month of one another on the streaming service. The others are “Rustin,” a biopic about a gay civil-rights-era activist, Bayard Rustin, and “American Symphony,”...