We demonstrate that the Casimir force between two dielectric slabs containing metallic wires will strongly depend on the relative orientation of the wires and can even change sign with rotation when an appropriate fluid is placed between the slabs. In this case, we find attractive-repulsive transitions for both slab orientation and relative position. We find that this effect occurs for experimentally realizable structures and realistic material dispersions down to sub-100nm surface-surface separations. We show that the attractive-repulsive transitions are qualitatively predicted by a simplified effective-medium theory.