What cosmic ray ionisation rate is required such that a non-ideal magnetohydrodynamics (MHD) simulation of a collapsing molecular cloud will follow the same evolutionary path as an ideal MHD simulation or as a purely hydrodynamics simulation? To investigate this question, we perform three-dimensional smoothed particle non-ideal magnetohydrodynamics simulations of the gravitational collapse of rotating, one solar mass, magnetised molecular cloud cores, that include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of $a_text{g} = 0.1mu$m, and our free parameter is the cosmic ray ionisation rate, $zeta_text{cr}$. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with $zeta_text{cr}gtrsim10^{-13}$ s$^{-1}$ are indistinguishable from ideal MHD models and the evolution of the model with $zeta_text{cr}=10^{-14}$ s$^{-1}$ matches the evolution of the ideal MHD model within one per cent when considering maximum density, magnetic energy, and maximum magnetic field strength as a function of time; these results are independent of $a_text{g}$. Models with very low ionisation rates ($zeta_text{cr}lesssim10^{-24}$ s$^{-1}$) are required to approach hydrodynamical collapse, and even lower ionisation rates may be required for larger $a_text{g}$. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionisation rate. However, realistic cosmic ray ionisation rates approach neither limit, thus non-ideal MHD cannot be neglected in star formation simulations.
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