We study the influence of non-magnetic impurities on the phase diagram of doped two-leg Hubbard Cu–O ladders. In the absence of impurities, this system possesses d-wave superconducting states and orbital current states depending on the doping. A single, strong, scatterer modifies its environment locally and this effect is assessed using a renormalization group (RG) analysis. At high doping, disorder causes intraband instabilities and at low doping it promotes interband instabilities. In the former case, we extend the boundary conformal field theory method—developed in the context of single chains—to handle the ladder problem, and we find exact closed-form analytical expressions for the correlation functions. This allows us to compute experimentally measurable local quantities such as the nuclear magnetic resonance line broadenings and scanning tunneling microscope profiles. We also discuss the low-doping regime where the Kondo physics is at play, making qualitative predictions about its nature. Insight into collective effects is also given in the many weak impurities case, based on an RG approach. In this regime, one sees the interplay between interactions and disorder. We emphasize the influence of the O atoms on disorder effects both for the single- and for the many-defect situations.