Summary: An appropriate gauge-invariant framework for the treatment of magnetized curvature and entropy modes is developed. It is shown that large-scale magnetic fields, present after neutrino decoupling, affect curvature and entropy perturbations. The evolution of different magnetized modes is then studied across the matter–radiation transition both analytically and numerically. From the observation that after equality (but before decoupling) the (scalar) Sachs–Wolfe contribution must be (predominantly) adiabatic, constraints on the magnetic power spectra are deduced. The present results motivate the experimental analysis of more general initial conditions of cosmic microwave background (CMB) anisotropies (i.e. mixtures of magnetized adiabatic and isocurvature modes during the pre-decoupling phase). The role of the possible correlations between the different components of the fluctuations is partially discussed.