We consider the color spin locking (CSL) phase of two-flavor quark matter at zero temperature for nonlocal instantaneous separable interactions. We employ a Lorentzian-type form factor allowing a parametric interpolation between the sharp [Nambu-Jona-Lasinio (NJL) model] and very smooth (e.g. Gaussian) cutoff models for systematic studies of the influence on the CSL condensate the deviation from the NJL model entails. This smoothing of the NJL model form factor shows advantageous features for the phenomenology of compact stars: (i) a lowering of the critical chemical potential for the onset of the chiral phase transition as a prerequisite for stability of hybrid stars with extended quark matter cores and (ii) a reduction of the smallest pairing gap to the order of 100 keV, being in the range of values interesting for phenomenological studies of hybrid star cooling evolution.