  Using the Bower-Liang model, we discuss how pressure anisotropies affect the
microscopic and macroscopic properties of hybrid stars. We find that
anisotropies affect the maximum mass, central density, and radius of the
canonical stars. Anisotropies also affect the minimum neutron star mass that
presents quarks in their core, as well as the total amount of quarks for the
maximally massive stars. We also confront our results with standard
constraints, such as the radius and the tidal parameter of the canonical star,
as well as the mass and radius of the PSR J0740+6620 pulsar. We observe that
moderate values for anisotropies could fulfill these constraints
simultaneously. On the other hand, within more extreme degrees of anisotropies,
more speculative constraints such as black widow pulsars PSR J0952-0607 and the
mass-gap object in the GW190814 event can be explained as hybrid stars. We also
investigate the role of anisotropies in the neutron stars' moment of inertia.
