Non-linear biomolecular interactions on the membranes drive membrane remodeling that underlies fundamental biological processes including chemotaxis, cytokinesis, and endocytosis. The multitude of biomolecules, the redundancy in their interactions, and the importance of spatiotemporal context in membrane organization hampers understanding the physical principles governing membrane mechanics. A minimal, in vitro system that models the functional interactions between molecular signaling and membrane remodeling, while remaining faithful to cellular physiology and geometry is powerful yet remains unachieved. Here, inspired by the biophysical processes underpinning chemotaxis, we reconstituted externally-controlled actin polymerization inside giant unilamellar vesicles, guiding self-organization on the membrane. We show that applying undirected external chemical inputs to this system results in directed actin polymerization and membrane deformation that are uncorrelated with upstream biochemical cues, indicating symmetry breaking. A biophysical model of the dynamics and mechanics of both actin polymerization and membrane shape suggests that inhomogeneous distributions of actin generate membrane shape deformations in a non-linear fashion, a prediction consistent with experimental measurements and subsequent local perturbations. The active protocellular system demonstrates the interplay between actin dynamics and membrane shape in a symmetry breaking context that is relevant to chemotaxis and a suite of other biological processes.