The theme for DaVinci’s Demons is a musical palindrome. Outside the short Symmetry, I think Nolan’s Memento might be the closest thing I’ve seen to a palindrome in film. According to Wikipedia there are a couple of palindrome novels, apparently difficult to read. There are a few poems and an essay that create a pessimistic forward-read and an optimistic backward-read. I haven’t found a story that can be read forwards and backwards by section or chapter.
For some reason I misread a screenshot of this page in the feed as “Best of Nuns."