Jamming of granular media has been shown to possess the property of stiffness variation, transitioning from a soft to a quasi-solid state depending on the packing density of the granules. Recently, a gradual stiffness change for bending has been reported by using compliant, cubic shaped granules. Here we demonstrate that the same method and material also exhibits a gradual stiffness change for compression. As a potential application of "compliant jamming", a bio-inspired robotic platform with jamming membranes as end effectors is designed and tasked with climbing straight vertical shafts. First, the benefit of varying the bending stiffness is investigated in the climbing task by measuring the friction force that the end effectors are applying to the shaft walls, especially if the walls are irregularly shaped. Then the role of compressive stiffness variation is explored by analyzing the performance of the robot in the climbing task, showing multi-modal properties of jamming membranes: (i) enabling a pressure sensor to detect the shaft walls, acting (ii) as grippers that actively use the irregularities of the walls to climb up by state-switching the granular material and (iii) as force dissipators that can dissipate internal forces caused by closed kinematic chains.