As others have hinted, Hollywood leans left in its personal life, but the actual product it puts out is remarkably spread across the spectrum. Let's look at ideology (or lack thereof) in the top 10 grossing movies of all time. Not adjusting for inflation will give more weight to recent pictures:
1. Avatar: unambiguously left, very environmentalist
2. Titanic: unambiguously left
3. Marvel's Avengers: right, celebrates extreme wealth, defense spending, etc.
4. The Dark Knight: Very right
5. Star Wars Episode I: leans right, celebrates traditional religion and international intervention, condemns bureaucracy
6. Star Wars: leans right, government is a force for evil, also has devoutly religious people in a very unexpected setting
7. The Dark Knight Rises: Very right
8. Shrek 2: seems entirely non-ideological
9. E.T. the Extra-Terrestrial: mostly non-ideological
10. The Hunger Games: Catching Fire: unambiguously right, as others have pointed out
So that's 4 movies with right wing themes + 2 movies that seem to lean right against 2 movies with left wing themes.
Most of these movies are ambiguous. I don't even think the Nolan Batman movies are rightwi-ng.