Focusing on primitive icy minor bodies in the solar system like cometary nuclei, centaurs, transneptunian objects (TNOs), and main-belt comets (MBCs) we investigate the stability of these objects against rotational breakup by comparing their location in (radius – rotational period) space with respect to separation lines of the stable and breakup zones in this plane. We estimate the bulk tensile strength according to new structural and elasto-mechanical models of grain-aggregates, using these tensile strengths to compute separation lines. We note that the process of grain coagulation and growth is highly uncertain in the field of solar system formation and we simply don't know how to grow interstellar grains to aggregates larger than about 1 mm but we apply in our calculations the recently available elasto-mechanical models of grain-aggregates. Accorging to this study most of the observed comets, centaurs, TNOs, and MBCs are stable against rotational breakup, with a few notable exceptions. E.g., we suggest that the rotational fission is a likely scenario for the Haumea-family in the Kuiper belt.