Palaeomagnetism of climatically sensitive sedimentary rock types, such as glacial deposits and evaporites, can test the uniformitarianism of ancient geomagnetic fields and palaeoclimate zones. Proterozoic glacial deposits laid down in near-equatorial palaeomagnetic latitudes can be explained by 'snowball Earth' episodes, high orbital obliquity or markedly non-uniformitarian geomagnetic fields. Here I present a global palaeomagnetic compilation of the Earth's entire basin-scale evaporite record. Magnetic inclinations are consistent with low orbital obliquity and a geocentric-axial-dipole magnetic field for most of the past two billion years, and the snowball Earth hypothesis accordingly remains the most viable model for low-latitude Proterozoic ice ages. Efforts to reconstruct Proterozoic supercontinents are strengthened by this demonstration of a consistently axial and dipolar geomagnetic reference frame, which itself implies stability of geodynamo processes on billion-year timescales.