It really depends on the state. My family moved from FL to CA while I was in Baltimore for school. I was not a MD resident because my family, as my financial support (their main criteria) was in CA. In CA, the rules are pretty strict, something about physically being there for x number of years - and frankly, I really didn't want to be applying as a CA resident anyway. So, I ended up moving to TN! 🙂
So I would check the requirements in GA. Since you're not going to be physically spending any time in the new state, I doubt that you could be counted as a resident there. But I think there's a good chance that you'd be a GA resident, even if your parents move - you live (and maybe work?) there now, you probably have a driver's license/voting card, etc. Hopefully, that would be enough. And even if it doesn't pan out, I would go ahead and apply to GA state schools anyway - a lot of the time, state schools will give extra consideration to people who are technically out-of-state, but have some sort of connection to the state.
Good luck!