The correct solution would be to check "Normals_Forward" on all your shader nodes for the hair. This includes the root node, and any additional lighting nodes that may be there in more complex shaders.

The back side of a polygon used to be (in P5) handled the same as the front side. In P6 and P7 they are not, and you have to request explicitly that it be handled the old way. The old way is "Normals_Forward" - in other words, even if you're looking at the "back" of a polygon, pretend its the front and shade it the same.

Any materials designed on or for P5 don't even have that option because it was created later. As a result, materials need to be updated in order to behave the same.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)