Why do conservatives hate Hollywood?

[Skill and Chance]

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.

[Skill and Chance]

I'm not sure than opposing the system is right-wing. It can be a very left-wing position, too.

I assume you're talking about Hunger Games and Star Wars?  But it goes beyond that.  In the Hunger Games because the rural poor are shown as better off supporting themselves by hunting, small business, etc. and in Star Wars because the protagonists are out to preserve and later revive traditional religion against a government that oppresses it severely.  Although SW is more ambiguous because there are some explicit digs at Bush in Episode III for example.  But still the overall thesis of SW is religious freedom and the overthrow of an increasingly tyrannical government. 

[Skill and Chance]

That seems like an odd element of the setting of The Hunger Games to focus on when the entire premise of the franchise involves staggering wealth inequality presented as a monstrous evil.

Yes, but it's more the Tea Party railing against lobbyists in mansions in the DC suburbs, not the left railing against the Koch brothers and Wall Street.  Remember that families expose their children to greater risk the more handouts they take and can only save themselves by being self-sufficient.  That's explicitly conservative on economics, granted with a pacifist streak.

[Skill and Chance]

I'm just having some fun here, guys.  Don't take it too seriously.  Only the Dark Knight and Avatar on that list could be considered truly, consistently ideological.  But it's an interesting thought process nonetheless.