The quantum spin-1/2 two-leg ladder with an anisotropic XYZ Heisenberg intra-rung interaction and Ising inter-rung interactions is treated by means of a rigorous approach based on the unitary transformation. The particular case of the considered model with X-X intra-rung interaction resembles a quantum compass ladder with additional frustrating diagonal Ising interactions. Using an appropriately chosen unitary transformation, the model under investigation may be reduced to a transverse Ising chain with composite spins, and one may subsequently find the ground state quite rigorously. We obtain a ground-state phase diagram and analyze the interplay of the competition between several factors: the XYZ anisotropy in the Heisenberg intra-rung coupling, the Ising interaction along the legs, and the frustrating diagonal Ising interaction. The investigated model shows extraordinarily diverse ground-state phase diagrams including several unusual quantum ordered phases, two different disordered quantum paramagnetic phases, as well as discontinuous or continuous quantum phase transitions between those phases.