Most types of outdoor fabrics on the market will be mold-resistant acrylic or olefin. Naturally resistant to moisture, they fare better than more natural materials.
Olefin, sometimes referred to as polypropylene fiber is seriously durable and easy to clean so a great choice for a busy family focused backyard. Standard polyester is washable, tough and versatile. It is resistant to stretching and mold and can be created in a whole range of colors and patterns to go with whatever color scheme you have in your outside space.