Tom Laughlin's Billy Jack was slowly overshadowed/overwhelmed by Laughlin's political views. Many a war is waged on Straw, especially if it's anyone on the opposite end of Laughlin's political views. The sequels gradually swapped out much of their predecessor's face-kicking action for even more heavy-handed pontificatingr.
Most people assume The Birth of a Nation, which portrays The Klan as heroic saviors, was a tract by director D. W. Griffith. In fact, it's an adaptation of the then-popular novel The Clansman by Thomas F. Dixon, Jr, which was itself a racist author tract. Being the son of a Confederate Army colonel, Griffith may have bought into the novel's revisionist history, but he denied having any ulterior motive for making the movie.
In response to criticism against Birth of a Nation, Griffith's next movie Intolerance definitely was an author tract against class-based prejudice, religious discrimination, and sexism.
The Blot by Lois Weber is all about attacking the sub-poverty wages given to university professors, going so far as to quote magazine editorials. The whole plot concerns the struggle of Prof. Griggs's family to survive. His daughter faints from hunger and his wife steals a chicken from the neighbors (but she puts it right back).
Richard Linklater's film version of the non-fiction book Fast Food Nation went from an exposé of the practices of the fast food restaurant industry to a two-hour rant about why people shouldn't eat meat. Despite becoming an In Name Only adaptation of the book, author Eric Schlosser (who is not a vegetarian) still endorsed the final product (which may not be that surprising when one considers that the original book is below and its ideas are not that different).
Glen or Glenda is essentially Ed Wood's exploration of gender non-conforming people like himself; he even played the title character under a pseudonym.
At the end of Charlie Chaplin's The Great Dictator, Chaplin gives a Rousing Speech where he more or less steps out of character and urges the viewers to resist the Nazis. Given that France was invaded during its production, this use of the trope is very understandable.
Persecuted is largely one long sermon on the claim that Christians are persecuted in America.
Akira Kurosawa had a very low opinion of the scandal-mongering tabloids that became very prominent in post-war Japan. The result was Scandal a story about scummy tabloid journalists who incorrectly accuse an artist and a singer of having an affair.
Seed of Chucky is this for the creator Don Mancini, an openly gay man, who used the film to describe is coming out experiences and what it felt like. The movie sets aside horror for horror-comedy and family drama. In a killer doll movie of all things.
Uwe Boll's Rampage films are a particularly weird breed of an Author Tract. Its Evil GeniusVillain Protagonist Bill Williamson is a deranged psychopath and domestic terrorist who, while Going Postal, murders innocent people by the dozens for nothing but his own self-serving reasons. However, at least once per film, he'll go on a minutes-long rant explaining that his violent actions are supposed to wake up humanity, giving a very thought-out analysis about political and economic corruption.
Frank Capra freely admitted that It's a Wonderful Life was created in part with the intention of combating a modern trend towards atheism. That hasn't stopped it from becoming a widely beloved Christmas classic which is often enjoyed by religious and secular people alike, however.