The high-density behavior of stellar matter composed of nucleons and leptons under equilibrium and charge neutrality conditions is studied with the Skyrme parametrizations shown to be consistent (Consistent Skyrme Parametrizations, CSkP) with nuclear matter, pure neutron matter, symmetry energy and its derivatives in a set of 11 constraints [Dutra et al., Phys. Rev. C 85, 035201 (2012)]. The predictions of these parametrizations on the tidal deformabilities related to the GW170817 event are also examined. The CSkP that produce massive neutron stars give a range of for the canonical star radius, in agreement with other theoretical predictions. It is shown that the CSkP are compatible with the region of masses and radii obtained from the analysis of recent data from LIGO and Virgo Collaboration (LVC). A correlation between dimensionless tidal deformability and radius of the canonical star is found, namely, , with results for the CSkP compatible with the recent range of from LVC. An analysis of the graph shows that all the CSkP are compatible with the recent bounds obtained by LVC. Finally, the universal correlation between the moment of inertia and the deformability of a neutron star, named the I-Love relation, is verified for the CSkP; it is also shown to be consistent with the prediction for the moment of inertia of the PSR J0737-3039 primary component pulsar.