Lattice simulation of QCD at small net baryon densities and high temperature have revealed that the transition from the hadronic phase to the deconfined quark-gluon plasma is a crossover. Recently, the structure of neutron stars have been studied with a crossover equation of state by means of a switching function to model a smooth transition from a pure neutron matter to massless quarks. The switch function parameter was constrained in order to reproduce neutron stars up to about two solar masses, with the constraint that the adiabatic sound velocity cannot exceed the speed of light. Following the same line, such a study has been extended by considering the relevance of color superconducting massless quarks in the cold dense matter. In this contribution, we investigate the crossover phase transition into hybrid compact stars by means of an equation of state which incorporates hadronic matter, composed by nucleons, hyperons and $\Delta$-isobars degrees of freedom, massive quark matter with the inclusion of non-perturbative effects and leptons in $\beta$-stable equilibrium.