We analyze theoretically the polarization dynamics in unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). The master VCSEL is subject to an isotropic optical feedback. The slave VCSEL is subject to an orthogonal optical injection from the master VCSEL, i.e., only the linearly polarized mode orthogonal to the dominant linearly polarized mode of the free-running slave VCSEL is injected into the slave VCSEL. This laser configuration may lead the slave VCSEL polarization to switch to that of the injected master laser field. The injected power required for polarization switching depends on the frequency detuning. We identify in the plane of the injection parameters two regions of enhanced synchronization between the injected LP mode and the corresponding slave LP mode. In the so-called region II the slave VCSEL exhibits anticorrelated dynamics in its two LP modes while in the so-called region I the slave VCSEL exhibits dynamics in only one LP mode, which corresponds to the polarization of the injected field. The two regions exhibit different synchronization properties in both the LP mode dynamics and total intensity dynamics. We furthermore analyze the dependency of the synchronization quality on the parameter mismatch between master and slave VCSELs and on the polarization switching properties of each VCSEL.