The most likely cause for white shirts to go pink is a dye transfer, where the clothes picked up red dye from something in the washer. White shirts that have pink stains can generally be returned to pristine shape, but it takes a lot of work and some shirts may have pink traces remaining. If your shirt says dry-clean only, try your luck at the dry cleaner's so you don't ruin the item. Tackle all other dye transfers at home.
Rub heavy-duty liquid laundry detergent over the pink blotches, to cover them.
Rinse the white shirt in your utility sink until the laundry detergent washes out and the water runs clear. Check the stain. This may have gotten it out, but if not there's still hope.
Prepare a bleach solution in a 5-gallon bucket by mixing 1/4 cup of chloride bleach with 1 gallon of cool water. Pop the pinkish shirt in the laundry solution and let it soak for half an hour.
Pull the shirt out of the bleach solution and rise it again under cool water.
Wash the shirt in your washing machine following the directions on the shirt's care tag. Machine dry the shirt or hang it to dry.