|If you mean real white spots, the only answer is bleach. Chlorine bleach is the worst culprit, but it you aren't using liquid chlorine, be aware that many detergents have various types of bleach in them. Others have enzymes to remove organic stains, and if the t-shirts have organic dyes they can be affected if detergent is sprinkled on damp clothing.
If they aren't "white" spots, but just light spots, it may be detergent sprinkled on damp clothing is taking out some residual soil, leaving the rest of the shirt still premeated with deposited soil. When Fuller introduced the concentrated Fuller 86, despite instructions to the contrary, some people sprinkled it on top the clothing while the washer was filling, then found "white" or light spots, which were actually clean places where Fuller's superior cleaning product had taken out spots of redeposited soil, fillers, etc. that many other detergents leave behind.
Nothing will remove bleached spots; but if they are actually "clean" spots, soak in detergent and warm or hot water for an hour, agitating occasionally, then rinse as normal.
The solution to most spotting is to dissolve and mix detergent and bleach before adding clothing. Automatic bleach dispensers are often the culprit, particularly if one is malfunctioning, or if you over-fill the washer.
One other possibility could be residue from concentrated softeners, dryer sheets or spray starch spatters, but these would come out with repeated washing.