Surfaces that are strongly nonwetting to oil and other low surface tension liquids can be realized by trapping microscopic pockets of air within the asperities of a re-entrant texture and generating a solid-liquid-vapor composite interface. For low surface tension liquids such as hexadecane (gamma(lv) = 27.5 mN/m), this composite interface is metastable as a result of the low value of the equilibrium contact angle. Consequently, pressure perturbations can result in an irreversible transition of the metastable composite interface to the fully wetted interface. In this work, we use a simple dip-coating and thermal annealing procedure to tune the liquid wettability of commercially available polyester fabrics. A mixture of 10% 1H,1H,2H,2H-heptadecafluorodecyl polyhedral oligomeric silsesquioxane (fluorodecyl POSS) and 90% polyethyl methacrylate (PEMA) is used to uniformly coat the fabric surface topography. Contact angle measurements show that a robust metastable composite interface with high apparent contact angles can be supported for hexadecane (gamma(lv) = 27.5 mN/m) and dodecane (gamma(lv) = 25.3 mN/m). To tune the solid surface energy of the coated surface, we also developed a reversible treatment using thermal annealing of the surface in contact with either dry air or water. The tunability of the solid surface energy along with the inherent re-entrant texture of the polyester fabric result in reversibly switchable oleophobicity between a highly nonwetting state and a fully wetted state for low surface tension liquids such as hexadecane and dodecane. This tunability can be explained within a design parameter framework, which provides a quantitative criterion for the transition between the two states, as well as accurate predictions of the measured values of the apparent contact angle (theta*) for the dip-coated polyester fabrics.