To try to capture all of the horrible fictional films out there that have a "message" and put them into one post would be a viral listicle on its own. The reason is simple: these films don't exist to entertain, they exist to push a point of view. This rarely works in my experience.
Books like "Atlas Shrugged" and "1984" are timeless classics because they don't beat you over the head with the politics or ideology. What they do is much more difficult and much more effective: through storytelling they reveal what they believe to be absolute truth and allow the viewer to connect the dots to their own life or current events. But the key is that it has to be entertaining even if the reader is too dense to make any connections at all. This applies to film as well.
In fact, it applies even when the message isn't political or ideological at all. Take 2010's "Inception" which is a mind trick film about adventures in people's dreams. Wonderful science fiction. But did you realize the entire film was a metaphor for filmmaking? Or that the Big Lebowski is about castration?
Once the symbolism is pointed it's hard to deny and in hindsight appears obvious. This is how messaging in a film is done right.
For examples of how it's done wrong, check out DC/911 or Lions for Lambs. Two films with opposing ideological perspectives on the war on terror that could've been scrutinized by campaign finance reformists they were dripping with so much obvious partisanship.
Last week I was given the opportunity to see "The Giver," a film based on the famous book by Lois Lowry. A quick glance at the cast which included screen legends Meryl Streep and Jeff Bridges would make one quick to believe that if a message were to be had, it would echo the common Hollywood refrain. "Make love not war, climate change" etc etc.
But if you know anything of the book, which I did not until after seeing the film, you'd know this has a message that is much more centered around government control, education, and even abortion. I'll refrain from giving away the plot points (as this is not a review) but I must say that the film masterfully entertains viewers and draws them into a fantasy world, reveals what the filmmakers/writers believe to be the truth, and then the characters pursue that truth. Simple and elegant. No beating over the head, no nauseating speeches with thinly veiled attacks on politicians. Just a great story that makes you think. Exactly how filmmaking should be.
One of the reasons that this fairly simple process is so difficult for filmmakers to grasp is because people are passionate. They want others to think like them and when they're pushing their idea, it's hard to hold back. They really want to make sure people don't miss it.
But truth doesn't always work that way. People can walk away from the Big Lebowski and be utterly entertained without knowing a thing about any underlying symbolism about castration. In fact, I'd think it were preferable. What you want is for people to walk away with an impression. An understanding. Not a desire to donate to a political party. They can get the truth you're trying to reveal to them without having to be sat down and spoon fed the points.