When it was announced last year that Fr. James Martin, SJ, was being brought in as a “consultor” to the Vatican’s communications team, reactions were predictably on a spectrum ranging from deeply perplexed to blood-vessel bursting outrage. Known for his role as editor-at-large for the far-left Catholic rag America Magazine as well as his boundary-pushing views on the Church and homosexuality, Fr. Martin is the kind of name that gets an instant reaction when brought up in any conversation. And among orthodox Catholics, it’s decidedly not a positive one. Fr. Martin became the second high-profile Jesuit to join the Vatican’s propaganda arm,...