We demonstrate all-optical linear-polarization control in semiconductor microcavities using an exciton-polariton condensate in an elliptically shaped optical trap. The microcavity inherent TE-TM splitting lifts the pseudospin degeneracy of the anisotropic trap ground state. The emerging fine-structure modes are shown to be polarized linearly parallel and perpendicular to the trap major axis. We demonstrate polariton condensation into the excited pseudospin mode with a high degree of linear polarization, which rotates as we rotate the trap. We then extend our study to a system of two coupled linearly polarized condensates and demonstrate rich spin dynamics reflecting spontaneous synchronization and high correlation between the condensate pseudospins as a function of the pump parameters. Our findings open up exciting perspectives in both spinoptronics and studies on extended systems of interacting nonlinear optical elements with anisotropic coupling strength and adjustable fine structure.