Not sure what was conservative about it.
It's also interesting that some of the districts raised their kids to believe in the honor of fighting in the Games. Again the underlying message was not hard to spot. These districts represented military families and military culture and patriotic institutions like the Marine Corps that are committed to the honor of fighting on behalf of the nation. The movie was slighting these people or suggesting that they are misguided or suckers.
Naturally it was the gung-ho pledges from these districts who were the main bad guys once the Games got underway. They banded together into a WASPy little gang that hunted down and killed the other pledges. Oh and by the way, the other pledges consisted of blacks and females and younger/poorer/weaker white kids. Anybody think there might be a message here?
Oh yeah, and then after Roux, the little black girl pledge, was killed by one of the white male pledges, there was a race riot in her home district. To complete the effect, the snappily uniformed all white police force hosed them down Civil Rights style. Hmm, I wonder what this could mean?
And of course the bad guys in the government were portrayed as stuffy aristocrats. The hostess lady was literally done up as a powdered Marie Antoinette. All of this to make sure that no skull full of mush could fail to understand that these were fundamentally class enemies, the One Percent.
But wait -- don't forgot the Lenny Kravitz character, Katniss's presumably gay "stylist" who functioned not only as the film's Magic Negro (per the LA Times definition) but also its Magic Gay Guy. He gave her the behind-the-scenes moral support she needed to fight the one percenters and win!