A polariser is quite good at blocking EM radiation, but not perfect.
No polariser is perfect, and does not block 100% of the radiation. This is typically specifed in terms of the extinction ratio. The best laboratory grade polarisers have extincition ratios of the order 100000:1 .
Such good polarisers are only possible over certain wavelengths, and for high-energy radiation (like x-rays, gamma rays), polarisers don't exist or have much lower efficiency. Additionally, for such types of radiation, the radiation itself could potentially damage the structure of the material itself.
Many types of harmful radiation are not electromagnetic, but rather high-energy charged particles, which are not blocked by polarisers.
For blocking thermal radiation from the outside to keep something, you also need to consider that the polariser emits its own thermal radiation, so you would need to cool it down. In this case, a metal heat shield in a cryostat is just as good. Thermos flasks that keep things warm need to reflect thermal radiation, whereas polarisers absorb it.