In planar microcavities, the transverse-electric and transverse-magnetic
(TE-TM) mode splitting of cavity photons arises due to their different
penetration into the Bragg mirrors and can result in optical spin-orbit
coupling (SOC). In this work, we find that in a liquid crystal (LC) microcavity
filled with perovskite microplates, the pronounced TE-TM splitting gives rise
to a strong SOC that leads to the spatial instability of microcavity polariton
condensates under single-shot excitation. Spatially varying hole burning and
mode competition occurs between polarization components leading to different
condensate profiles from shot to shot. The single-shot polariton condensates
become stable when the SOC vanishes as the TE and TM modes are spectrally well
separated from each other, which can be achieved by application of an electric
field to our LC microcavity with electrically tunable anisotropy. Our findings
are well reproduced and traced back to their physical origin by our detailed
numerical simulations. With the electrical manipulation our work reveals how
the shot-to-shot spatial instability of spatial polariton profiles can be
engineered in anisotropic microcavities at room temperature, which will benefit
the development of stable polariton-based optoeletronic and light-emitting
devices