What can cells gain by using disordered, rather than folded, proteins in the architecture of their skeleton? Disordered proteins take multiple co-existing conformations, and often contain segments which act as random-walk-shaped polymers. Using X-ray scattering we measure the compression response of disordered protein hydrogels, which are the main stress-responsive component of neuron cells. We find that at high compression their mechanics are dominated by gas-like steric and ionic repulsions. At low compression, specific attractive interactions dominate. This is demonstrated by the considerable hydrogel expansion induced by the truncation of critical short protein segments. Accordingly, the floppy disordered proteins form a weakly cross-bridged hydrogel, and act as shock absorbers that sustain large deformations without failure.