Washing your GORE-TEX® jacket will not hurt it. In fact, washing your jacket regularly will help maintain the DWR coating on the outside of the fabric, which causes water to bead up and shed off, rather than being absorbed.
Be sure to zip all zippers, and close all Velcro® fasteners before you wash your jacket. Please use a mild powder detergent. Liquid detergents can leave a residue on your jacket that will interfere with the DWR performance. You can wash your jacket in a regular washing machine, in cold water, on a gentle cycle. Put it through the rinse cycle twice, to be sure the detergent residue washes out. You can dry your jacket in a low temperature dryer, and if necessary, use a cool iron. Do not use bleach or fabric softeners, dry clean, or store when wet.