Welcome to electrostatics:
If you use a dryer, clothes become dry; yet the typical dryer basically is a rotating drum containing the clothes where clothes rub against each other. This creates both fine particles and «hairs» swirling around, and separates electric charges. Some of the particles end in the filter of the dryer, others remain with the clothes which -- because they are not metallic, and not good electric conductors -- do not discharge well with the metallic drum of the dryer. And this renders clothes like magnets for the small hairs and fibers (or, lint); synthetic clothes tend to be more prone to this, than cotton.
This where -- if you intend to use an electric dryer -- fabric softeners come into play, or the dryer sheet you mention to reduce the effect.
If you do not need the table clothes this quickly and have the space outside, or in a well ventilated space (e.g., below the roof, laundry room, basement), consider drying the clothes on a clothes line or rack prior to iron them / folding for the closet / drawer.