The Roman Catholic Church in the Philippines is facing a potential what could turn out to be something public-relations problem ahead of Pope Francis’ visit to the country this month, after an appeals court upheld a family-planning activist’s conviction for the crime of offending religious feelings.

Carlos Celdran’s offense was a typically colorful one for the well-known performance artist. In 2010, dressed in the kind of derby hat and long-tailed coat worn by the Philippines’ 19th-century independence hero José Rizal, he...