We experimentally study the mechanical pressure exerted by a set of respectively passive isotropic and self-propelled polar disks onto two different flexible unidimensional membranes. In the case of the isotropic disks, the mechanical pressure, inferred from the shape of the membrane, is identical for both membranes and follows the equilibrium equation of state for hard disks. On the contrary, for the self-propelled disks, the mechanical pressure strongly depends on the membrane in use, and is thus not a state variable. When self propelled disks are present on both sides of the membrane, we observe an instability of the membrane akin to the one predicted theoretically for Active Brownian Particles against a soft wall. In that case, the integrated mechanical pressure difference across the membrane can not be computed from the sole knowledge of the packing fractions on both sides; a further evidence of the absence of equation of state.