One of the most persuasive arguments in favour of vegetarianism is that meat metabolises to purines. They are most abundant in organ meats (offal) which apparently was the favourite treat in the Paleo days (brain and bone marrow in particular – the bits that big carnivores could not easily access). Purines are also in seafood (but also in chocolate). Tasty as they are, they contribute to gout and to kidney stones. Better to stay away from meat (chocolate is fine).
And indeed, quite a few Atkins followers report on various discussion forums that they had developed gout and had to stop the diet. High protein diet raises the level of uric acid in blood, but the kidney should handle that (actually there is no evidence on harmfulness of high protein diet on kidney function). Perhaps there are studies out there, I have not done extensive searches, but I one thing appears to make sense to me: sodium urate precipitates in more acidic conditions. High protein diet makes the blood more acidic. (Incidentlally, alcohol makes gout worse, possibly by acidifying the body even more). But if high protein diet is complemented by copious amounts of alkalising vegetables, thing should balance out. Something Atkins people might consider.
But why is it that Inuit/Eskimos have no gout, though they eat practically nothing but meat? Absence of salt in their diet? Vitamin D in the fish?