Tanning solutions work on dead animal skins, so I imagine that prolonged, repeated exposure would have some effect on living animal skin (a person's). Additionally, I read that different tree species' barks were used to tan hides into different colors (i.e: chestnut oak vs white oak, resulting in brown vs yellowish hides respectively). So is my hypothesis correct? Did historical writings on tanners ever mention that their hands were discolored from the hide tanning process?
Tannins do in fact stain the skin, though the degree of stain would depend on the method used (bark tanning is one of many methods), the dilution of the tannins in the solution, and the species of tree used.