  We generalize a recently proposed confining relativistic density-functional
approach to the case of density dependent vector and diquark couplings. The
particular behavior of these couplings is motivated by the non-perturbative
gluon exchange in dense quark matter and provides the conformal limit at
asymptotically high densities. We demonstrate that this feature of the quark
matter EoS is consistent with a significant stiffness in the density range
typical for the interiors of neutron stars. In order to model these
astrophysical objects we construct a family of hybrid quark-hadron EoSs of cold
stellar matter. We also confront our approach with the observational
constraints on the mass-radius relation of neutron stars and their tidal
deformabilities and argue in favor of a quark matter onset at masses below
$1.0~{\rm M}_\odot$
