You can wear anything you feel comfortable in. The idea isn't to get wet but to know that it is a possibility. Yoga pants and a moisture wick shirt or a bathing suit for warmer weather. In cooler months, or on rainy days, some like to wear a wetsuit or rash guard with some light SUP booties to stay warm.
An adventurous twist on Yoga, and a relaxing spin on stand-up paddle boarding. SUP Yoga (Paddleboard Yoga) is a variation of stand up paddle boarding (SUP), combined with yoga.