Polyester is a synthetic fiber resistant to shrinking, but it can still shrink if not cared for properly.
Polyester should generally be dried on a low heat setting and not over-dried. Over-drying can cause polyester to shrink or become misshapen.
It's always a good idea to check the care label on your polyester blanket or clothing before washing it, as different types of polyester may have different care requirements.
If you're unsure, it's best to err on caution and wash and dry your polyester items on a gentle cycle with low heat.