Texture mapping problems after reversing winding order

Every code example I’ve seen to reverse the winding order always keeps the UVs the same, and that’s how I’d been doing it for many months without any problems, but when I recently reversed the winding order of a mesh that was flipped after being imported from Blender, the texture no longer maps properly (it did on the original mesh even if everything was inside out - the texture details were nonetheless mapped to the right part of the body). Now, the texture is skewed so that the details for various body parts are on the wrong part of the body. I did a search again for code to reverse the winding order, but all the examples do the same thing that my own code does, so I’m not sure what the problem is.

Doesn’t anyone know why the texture will occasionally be screwed up when you reverse the mesh’s winding order? That usually doesn’t happen.