The Hodge dual of the anti-symmetric curvature tensor in four dimensions is another anti-symmetric curvature tensor. The Bianchi identity is the cyclic sum of three curvature tensors identically equal to the same cyclic sum of the three respective definitions of the same curvature tensors. So the Hodge dual of the Bianchi identity is a cyclic sum of curvature tensors with different indices, identically equal to the cyclic sum of their definitions. Quod erat demonstrandum.
This is one of several known points of breakdown of the Einstein field equation. We must end the ninety year era when these criticisms of the Einstein equation are just ignored by a self-serving faction.