The legal ability to ban breastfeeding at a business depends on state-specific law. Most states grant a mother the right to breastfeed in any location -- public or private -- in which she is authorized to be.

Sure, sure, you can legally do said thing almost anywhere in many states.

Much like I can legally be shirtless, as a man, almost anywhere in many states.

I can legally do these things in many places.

Neither of these things are protected classes. If these actions of mine cause others discomfort in a private establishment, I can be asked to leave as a result.

In such states, businesses cannot ban breastfeeding.

In general on paper, sure, but in practice, they absolutely can.

Unless breastfeeding is a protected class, just because you can legally do something does not mean a business cannot ask you to leave if they think you are making other customers uncomfortable.

In Georgia, breastfeeding is not a protected class.