Riverside, a liberal Protestant church known for its history of social-justice advocacy, has hosted world leaders such as Nelson Mandela,Martin Luther King Jr., Desmond Tutu and Bill Clinton. “I know that this church is begging for new life,” said Dr. Butler, 45 years old. “That process of resurrection involves some dying. This is what we believe in our Christian tradition.” One-on-one, Dr. Butler is witty and self-deprecating, and her sermons tend to be about 10 minutes shorter than those of her predecessors, congregants say.