We analyze different stages of magnetized quark star evolution incorporating baryon number conservation and using an anisotropic energy-momentum tensor. The first stages of the evolution are simulated through the inclusion of trapped neutrinos and fixed entropy per particle, while in the last stage the star is taken to be deleptonized and cold. We find that, although strong magnetic fields modify quark star masses, the evolution of isolated stars needs to be constrained by fixed baryon number, which necessarily lowers the possible star masses. Moreover, magnetic field effects, measured by the difference between the parallel and perpendicular pressures, are more pronounced in the beginning of the star evolution, when there is a larger number of charged leptons and up quarks. We also show that having a spatially varying magnetic field allows for larger magnetic fields to be supported.