Black hole X-ray binaries exhibit different spectral and timing properties in different accretion states. The X-ray outburst of a recently discovered and extraordinarily bright source, Swift J1727.8-1613, has enabled the first investigation of how the X-ray polarization properties of a source evolve with spectral state. The 2-8 keV polarization degree was previously measured by the Imaging X-ray Polarimetry Explorer (IXPE) to be ≈4% in the hard and hard intermediate states. Here we present new IXPE results taken in the soft state, with the X-ray flux dominated by the thermal accretion disk emission. We find that the polarization degree has dropped dramatically to ≲1%. This result indicates that the measured X-ray polarization is largely sensitive to the accretion state and the polarization fraction is significantly higher in the hard state when the X-ray emission is dominated by upscattered radiation in the X-ray corona. The combined polarization measurements in the soft and hard states disfavor a very high or low inclination of the system.