A white shirt is supposed to be just that: white! No other shirt colour begs to stay true to its colour or remain without spots or stains than a white shirt. Getting a white cotton polyester blend shirt white again really isn't different than getting a white cotton shirt white again. However, there are three important things you can do that will do more to get that shirt white again than the usual laundering you do to get it clean.
Dab the spot immediately with a dry, highly-absorbent material, drawing away whatever is potentially staining the white shirt. Wet and wring a highly-absorbent material and then blot the spot, again drawing away whatever is potentially staining the shirt.
Run water directly through the stain on the shirt. Gently rub the stain while the water is running through it.
Soak the shirt in water. Gently pull the shirt through the water every once in a while, so that it loosely moves through the water.
Pour or spray a laundry cleaner or stain pre-treater onto the spot. Gently rub it into the spot.
Let the laundry cleaner absorb into the cotton and polyester blend for at least several minutes. Rinse the spot clean.
Repeat pretreatment of the stain if necessary. Launder the shirt in the warmest water that's safe for it.
Fill the wash tub with warm to hot water. Pour laundry cleaner into the tub of water.
Pour laundry bleach or whitener into the tub of hot water, according to the appropriate bleach or whitener to water ratio. Wash the white cotton polyester shirt with like colours and fabrics or separately.
Rinse the laundry clean. Repeat laundering the shirt to get it whiter if necessary.