As you can see in the picture, when mining something light grey, the antialiasing combines the light and dark gray to make it white if there is not enough space to separate the colors. On the right face of the block that is being mined, this affect is present.
A solution is to antialias the mining block overlay separately from the stone block, and then merge the textures.
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Is this still a concern in the latest Minecraft version 13w48b? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.