That is a rather odd request. How exactly were you planning to connect FS and sci-fi with cultural anthropology anyhow?
It may be possible to make connections from the "comparative anthropology" standpoint- you'd have to consider the impact that space colonization, the subspace drive, contact with intelligent alien species, and so on would have had on human civilization. FreeSpace 1 and 2 each have a bit of background info on all involved cultures, but it probably isn't enough to assemble a reasonable paper on; taking user-made content into consideration, though (especially Blue Planet), and you may be on to something.
The biggest thing to consider when analyzing a future society, such as the human societies portrayed in FreeSpace, is that what is presented is highly speculatory. I'd say treat the games like novels, and consider any salient cultural factors within the context of the given world.
tl;dr You may be on to something, but you'll almost certainly need to pull material from Blue Planet if you want to have enough information to really work with. Plus, you may want to get instructor approval before proceeding with this.