There is no kidney issue with the Atkins diet. This was a rumor started by people who didn't think the diet would be healthy.
There is absolutely no evidence for it--not one single study shows that a high-protein, low-carbohydrate diet damages normal kidneys. If you have severe kidney disease, of course, you do have to restrict sharply your protein intake and probably shouldn't be doing Atkins or any other diet on your own.
From the Atkins site:
"Fallacy: You eat too much protein when doing Atkins, which is bad for the kidneys.
Fact: Too many people believe this untruth simply because it has been repeated so often that even intelligent health professionals assume it must have been reported somewhere.
But the fact is that it has never been reported anywhere. No one has as yet produced a study for review, or even cite a specific case in which a diet high in protein causes any form of kidney disorder. The only remotely related phenomenon is the fact that when someone is already suffering from far-advanced kidney disease, it is difficult for that persons body to handle protein. But protein has nothing to do with the cause of the kidney problem.