To me? It represents states' rights, and in a more symbolic nature, a unified flag that represents a more independent less-centralized form of power to oppose the American flag, which in my mind represents one large centralized form of power. It's a duality thing, which is exactly why my old class ring has an American flag on one side, and a confederate flag on the other.
The civil war was not fought over slavery alone. The people who claim that slavery was the only reason, or that it wasn't a reason or all, are wrong. It ties in heavily, but it's certainly not the only reason. That, however, shouldn't matter. Today, nobody here supports slavery (Or, no sane person, anyway. Hell, even the KKK doesn't go around saying it should be reinstated).
As a result of this, I feel the flag can keep all it's other meanings without being considered a "hey everybody, let's make slavery legal again!" symbol. Because, let's face it, a vast majority of people who use it don't support slavery, or even racism. They use it for other reasons- mainly southern ideals and occasionally other minor things, like a symbol of southern rock or what have you.
I would not call it an anti-American symbol. The CSA might have been anti-American, but they were following American ideals to the letter, even if for all the wrong reasons. They felt they weren't being represented, they felt trade policies heavily favoured the industrial north over the rural south, and they feared things would only get worse for them. So, they did the American thing to do- say "To hell with this, I'm leaving and making my own country". In all honesty, had I been alive at the time, I would have supported them if not for the whole slavery thing.