It's political in the same way something like 1984 is political. It's (mostly) not directly critiquing any specific ideology, but it is a fable of sorts, warning of dangers that can come from certain extreme behaviors and ideas. Both Cowslip's Warren and Woundwort's are pretty clear criticisms of giving up too much freedom or your own national identity in exchange for a faulty sense of security. Sandleford could be seen as a warning against not changing your ways until it's too late.
It's not direct commentary and can very well apply to any civilization, though, the Brits do have history fighting and dealing with these sorts of ideologies. Like 1984, it's a timeless story that anyone can take wisdom from at any point in history. Or not, it's all up to the reader.
Political doesn't have to conflict with mystical either. The movie isn't as dense as the book, and, in fact, I think the movie is less mystical. The book literally has a chapter by the name of Dea Ex Machina, which, of course, is a play on the Latin phrase "God out of the machine" where Hazel is, perhaps miraculously, put into a situation that saves him. But it's never directly shown to be any kind of supernatural force. Even Hazel being carried away at the end could be seen as a comforting hallucination Hazel has as he dies. It can never only be interpreted as one thing.
Basically, what I'm saying is, none of these themes or ideas are mutually exclusive, you can take a ton of different stuff out of the story, and basically everyone's gonna read it a little differently. That's part of what makes Watership Down so good. I love The Plague Dogs and other Adams novels, but few are as elegant yet dense with its themes as Watership Down.