To migrate, divide, and change shape, cells must regulate the mechanics of their periphery. The cell surface is a complex structure that consists of a thin, contractile cortical actin network tethered to the plasma membrane by specialized membrane-to-cortex attachment (MCA) proteins. This active and constantly fluctuating system maintains a delicate mechanochemical state which permits spontaneous polarization and shape change when needed. Combining in silico, in vitro, and in vivo experiments we show how membrane viscosity and MCA protein length regulate cortical dynamics. We reveal a novel mechanism whereby caging of linker proteins in the actin cortex allows for the amplification of small changes in these key parameters, leading to major alterations of cortical contractility. In cells, this mechanism alone gives rise to symmetry breaking phenomena, suggesting that local changes in lipid composition, in combination with the choice of MCA proteins, contribute to the regulation of cellular morphogenesis and function.