I was curious to know what it is about animal protein in general that would affect kidneys more than vegetable protein. So I went searching for a study.
There was a human intervention trial from the Dept of Internal Medicine in Texas that I found, which had evaluated animal protein-rich diet on kidney stones and calcium. The study took 15 subjects and fed them either vegetable protein, vegetable and egg protein or animal protein for 12 days in three different periods (1). What the study found was that the animal protein diet "conferred an increased risk for uric acid stones" but a lesser risk than the vegetarian diet for "calcium oxalate or calcium phosphate stones" (1).
Because my question really wasn't sufficiently answered by this study, I decided to pursue what National Kidney Foundation had to say. Finally, I found a publication they put out referencing nutrition and speaking to vegetarian diets in which they basically state that the veggie diets aren't "rich in higher quality protein" (2), but that also that the best sources of vegetarian protein may be ones lower in potassium and phosphorus depending on kidney dysfunction.
At best, the main focus on kidney health is a balance between protein and carbs because too few leads to more protein break down as well as protein with sodium (lower is better), phosphorus (lower is better), calcium, potassium (sometimes higher, sometimes low is better) and, of course, water amounts for keeping kidneys functioning well (2).
1. Breslau NA, Brinkley L, Hill KD, Pak, CY. J Clin Endocrinol Metab. 1988 Jan;66(1):140-6. Available at: http://www.ncbi.nlm.nih.gov/pubmed/2826524
2. National Kidney Foundation. Nutrition and Early Kidney Disease. Available at: http://www.kidney.org/atoz/pdf/NutriKidFail_Stage1-4.pdf