Superomniphobic surfaces display contact angles >150° and low contact angle hysteresis with essentially all contacting liquids. In this work, we report surfaces that display superomniphobicity with a range of different non-Newtonian liquids, in addition to superomniphobicity with a wide range of Newtonian liquids. Our surfaces possess hierarchical scales of re-entrant texture that significantly reduce the solid-liquid contact area. Virtually all liquids including concentrated organic and inorganic acids, bases, and solvents, as well as viscoelastic polymer solutions, can easily roll off and bounce on our surfaces. Consequently, they serve as effective chemical shields against virtually all liquids--organic or inorganic, polar or nonpolar, Newtonian or non-Newtonian.