Richard Adams always insisted that Watership Down is not an allegory: it is not a story about religion or politics, but a story about rabbits. If anyone should know what Watership Down is about, it is the author.
But a good story (and Watership Down is a great story) is true to life. The different rabbit societies strike the reader as being allegorical because they are true to what an advanced complacent society, or a repressive fascist society looks like. General Woundwart is a convincing evil dictator not because he is a thinly veiled Hitler or Stalin, but because he is an evil dictator.
The myths told in Watership Down are so moving because they serve the same function within the imaginary world of rabbits that myths serve in human society. Readers readily recognize parallels between myths of the rabbit hero Elhrairrah and our story of Adam and the Fall, or Moses and the Israelites in the desert, or Jesus himself. But Elhrairrah is not truly based on these characters. Parallels to Biblical characters can found throughout world religions, because these figures speak to deep human needs: the need to understand why we long to be good and happy and yet suffer; the need to understand what sort of people we are supposed to be; the need for hope in the face of evil and death.
Adams confesses to have been influenced by Joseph Campbell’s The Hero with a Thousand Faces, which compares common mythological themes across world religions. (Personally I found the book unreadable, but Bill Moyers’ interviews with Campbell are more interesting, and are readily found on YouTube.) Adams takes from Campbell the basic idea common to all mystical religions, that beyond every myth is an unknowable, but foundational reality with which the mystic comes into contact. Fiver the mystical rabbit enters trances, and comes out with fresh wisdom; the rabbits hear stories of Elhrairrah, the arch-type of all rabbits, and come into deeper contact with their own rabbitness, giving them the capacity to deal with the threats all around them.
Richard Adam’s protestations that Watership Down is not an allegory are very similar to J.R.R. Tolkien’s insistence that The Lord of the Rings is neither about the World Wars nor does it contain cryptic references to his Catholic faith. Both works are similar in the sense that they imagine worlds with their own internal mythologies and cultures, but which operate, mutas mutandis, according to the same moral and natural laws as our own. I think this is the source of their fascination: both works seem both familiar and strange, original and ancient, encouraging us to turn to familiar things (the woods and fields in Adams’ book, or tragic, mortal, humanity in Tolkein’s) with renewed wonder.