This is also true of novels. I've had people read various things into my novels - some of them intended, some of them not intended, some of which I approve, some of which I do not. But it's out of my hands by that point.

I seriously doubt the makers of The Lady Eve or Bringing Up Baby intended to say anything at all. They probably just wanted to entertain. Indeed, that is my motivation with my novels too. I don't self-consciously set out to insert any sort of message, as intentional preachiness is invariably insufferable. But what is important to me - and to anyone who takes such an approach - will be inherent in the text (or in the film) regardless.

Tolkien didn't intend any "message" in The Lord of the Rings (as he clearly states in his foreword) but people have invariably (and rightly) read into it things that were important to Tolkien. For instance, the importance of friendship, the extolling of cardinal virtues (courage, loyalty, sacrifice, etc), the battle between good and evil (not just external evil, but the evil within oneself - all the characters are tempted by the Ring), environmental concerns (the Ents versus Saruman), the horrors of war (he'd served in World War I and it shows during the siege of Gondor), and so forth. It's a damning condemnation of lust for power, and a powerful affirmation of his own Christian faith (specifically Catholic - look at the Army of the Dead stuck in a sort of purgatory, for instance). Above all, I'd say it's about the universally relatable melancholy of the end of an era, and about growing up (with Gandalf as Tolkien, and the hobbits as essentially his children).

Now I'm off to try and discern what unintended messages lurk within Wallace and Gromit: The Curse of the Were-Rabbit. :)