This isn't a 2A issue. The merchant has the right to refuse service to individuals but they do not have a right to discriminate against an entire group of people because of national origin.
CBI already has this covered. A friend of mine had her purchase delayed because of her green card. They couldn't instantly approve her purchase, but did an additional screen and she came back 24 hours to pick up her gun.
You may be able to sueas theDirector of Operations noted, but I personally prefer "voting with your feet" and not shopping there. I'm not familiar with the chain. Can you post some more info so that I can be sure to avoid them? I'll also give them a call to verify the policy.