Polyester will wash fine in your washing machine , it will not shrink and the colors will not run
probably nothing. polyester, won't shrink. follow the wash directions on the garment tag.
It won't shrink and the color won't run but if you want to keep the white really nice and white, I recommend Shout Color Catchers. It is a box of sheets (like dryer sheets) that you put in the wash and clothes never pick up colors from another garment. You can actually cut them in half to save cost. Any color that comes out in a wash load will be absorbed into the cloth. Have saved many items when inadvertently washed the something of another color that ran.
