The fence that separates humans and piggies symbolizes… separation. (That's the sort of insight you read Shmoop for, eh?)
Separation can be tricky, though. On the one hand, the fence keeps humans from corrupting piggies and violating the Prime Directive and making Mr. Spock mad. But on the other hand, you could see the fence as keeping the piggies in—preventing them from corrupting and hurting the humans. That's Human's view when he says, "Humans are filling up all the worlds. The humans build their stupid fence to keep us out, but that is nothing. The sky is our fence!" (14.195).
One of the reasons that Human says the fence "is nothing" is, as it turns out, that the piggies can get over the fence super easily by using an anesthetic grass. Rather than separation then, the fence shows the futility, or uselessness, of separation. What you want out gets in, just as (thanks to Miro and Ouanda) what you want in—all those technological goodies—gets out. Difference mixes; you can't control it.
At the same time though, trying to control it matters. The fence isn't about physical separation as much as it is about mental separation. For Lusitanians, it's a statement that the community has cast its lot with the sky; it's part of the Starways community. To turn off the fence means reforming the community—joining forces with its neighbors rather than with the imperialists in the sky.
Building different fences gives you different possibilities—the Bishop is eager for the chance to try to convert the piggies. But it also gives you different dangers, as Miro finds. He wants to climb the fence, and "become a renegade (16.197). And while he does become an outcast, it's not in the ways he might have expected: the fence paralyzes him, and suddenly he's an alien, unable to take part in his work or his life, cut off from his family and his former fiancé.
You can take down the fence, but there's always a new one with someone outside, it seems like. You can't have a community without someone left out.