  We examine the influence of the superconducting proximity effect on the
transport properties of a T-shaped double quantum dot strongly coupled to two
normal, nonmagnetic or ferromagnetic leads. We show that the two-stage Kondo
screening may be suppressed or enhanced by the presence of pairing
correlations, depending on the specific geometric arrangement of the device. We
explain our results by invoking effective decrease of Coulomb interactions by
proximity effect and find qualitatively correct description in many cases,
although spin-filtering effect stemming from spin-dependent Fano-Kondo
interference occurs to be surprisingly fragile to the presence of induced
pairing. The results are obtained within the numerical renormalization group
framework in the limit of large superconducting gap, which allows for a
reliable examination of the low-temperature sub-gap properties of the
considered system. Nevertheless, finite temperature effects are also taken into
account.
