It's actually fairly easy to topologise to prevent sorting issues. As later triangles in the triangle array will be drawn over earlier ones. Rather than disabling blackface culling, construct the triangle array from the outer spheres backfaces first (winding order reversed), then the inner spheres backfaces, then the inner spheres front faces, then the outer spheres backfaces. This will solve the sorting issue, and for a lot of hair topology the same setup works just as well.
This is an old PS1 era trick, often used for hair as you mentioned. You don't even need to carefully construct the triangle buffer, you can render it twice, one front face only and one back face only, with different render queue order. The catch is that it only works when you can predict the correct draw order. As soon as that order changes with the camera, or the geometry intersects itself or other transparent geometry, the trick breaks down.
it onyl works on objects that will be always facing the camera, or that can be rotated like a sphere
"blackface culling" is the funniest typo I've seen in ages.
I think 'blackface culling' is frowned upon these days