Combining single cell experiments, population dynamics and theoretical methods of membrane mechanics, we put forward that the rate of cell proliferation in E. coli colonies can be regulated by modifiers of the mechanical properties of the bacterial membrane. Bacterial proliferation was modelled as mediated by cell division through a membrane constriction divisome based on FtsZ, a mechanically competent protein at elastic interaction against membrane rigidity. Using membrane fluctuation spectroscopy in the single cells, we revealed either membrane stiffening when considering hydrophobic long chain fatty substances, or membrane softening if short-chained hydrophilic molecules are used. Membrane stiffeners caused hindered growth under normal division in the microbial cultures, as expected for membrane rigidification. Membrane softeners, however, altered regular cell division causing persistent microbes that abnormally grow as long filamentous cells proliferating apparently faster. We invoke the concept of effective growth rate under the assumption of a heterogeneous population structure composed by distinguishable individuals with different FtsZ-content leading the possible forms of cell proliferation, from regular division in two normal daughters to continuous growing filamentation and budding. The results settle altogether into a master plot that captures a universal scaling between membrane rigidity and the divisional instability mediated by FtsZ at the onset of membrane constriction. © 2022, The Author(s).