From my quick searching I've seen pretty mixed answers. The studies I found seemed to say that it didn't contribute to kidney stones, the extra water offset the extra oxalate and some even said the risk of kidney stones was lower. But that was for "moderate amounts".

Tea and coffee in moderation are not a problem. While tea and coffee do contain some oxalate, the extra fluid outweighs any possible disadvantage. In fact, some studies suggest that drinking moderate amounts of tea and coffee can actually lower the risk of kidney stones. In general, if you do drink caffeinated beverages, keep your daily amount of caffeine to no more than 400 milligrams. That's equal to four or five cups of regular coffee.

A meta-analysis based on 3 studies showed that the relationship between tea consumption and kidney stones was borderline nonlinear, with a 4% decrease in the risk of kidney stones for each 110 ml/day increase in tea consumption [15].

Interesting.

That's simply not true. If it was, the whole of Northern Ireland would be struck down with kidney stones. Tea is not great for you if you have them, but it doesn't cause them in everyone.