I've narrowed the problem down some. If I apply either the simple pbr or the procedural sss materials, I don't see the white eye problem. It is only when I use the sss w refracted eyes materials. Even when I apply on of the base materials to her body in the refracted eyes material group, her eyes go white. So it must be something particular to the refracted eyes material group.

Thanks for the suggestions. I'm not very proficient at using nodes yet, but I'll give your suggestions a try.