The bug

As can hopefully be seen in my screenshots, obvious straight lines can be seen through the stained/hardened clay.
This may be only in mesa plateau, or that may simply be the easiest place to see it as it is more flat. The seed I used was "mesa" for those examples, but I've tried several seeds and found signs of the same thing in every mesa I've visited.
Sometimes it can be less obvious due to less contrasting colors at the surface level. As can be seen from mesa2, where I've put wool to indicate the chunk boundaries, these lines are chunk related. It seems that there's a chunk-sized area where one "height" of colors meets another (strip going north-south) and in this strip the "sides" alternate every chunk, producing these "fingers" going east-west. On one side of the "strip" the colors are assigned by Y one off from the other side. In mesa3 and mesa4 you can see that the effect isn't just on the surface, and goes all the way down in the clay.

Code analysis

Based on 1.11.2 decompiled using MCP 9.35 rc1

It looks like the method net.minecraft.world.biome.BiomeMesa.getBand(int, int, int) is causing this by offsetting the used clay band index.