We analyze the shear strength and microstructure of binary granular mixtures consisting of disks and elongated particles by varying systematically both the mixture ratio and degree of homogeneity (from homogeneous to fully segregated). The contact dynamics method is used for numerical simulations with rigid particles interacting by frictional contacts. A counterintuitive finding of this work is that, the shear strength, packing fraction and, at the microscopic scale, the fabric, force and friction anisotropies of the contact network are all independent of the degree of homogeneity. In other words, homogeneous mixtures behave as segregated packings of the two particle shapes. In contrast, the shear strength increases with the proportion of elongated particles correlatively with the increase of the corresponding force and fabric anisotropies. By a detailed analysis of the contact network topology, we show that various contacts types contribute differently to force transmission and friction mobilization.