We investigate the spin behavior of the first excited state of a polariton condensate in an optical trap by means of polarization resolved spectroscopy. The interplay between the repulsive polariton interactions and the gain saturation results in a nontrivial spontaneous switching between the two quasidegenerate spatial modes of the polariton condensate. As a result, the polarization pattern of the emitted light dramatically changes. Successful harnessing of this effect can lead to a spin-demultiplexing device for polariton-based optical integrated circuits.