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We investigate the nature of the ULX M81 X-6, which has been suggested to harbour a neutron star (NS), by studying its long-term X-ray spectral and temporal evolution, using the rich set of available archival data from XMM-Newton, Chandra, NuSTAR, and Swift/XRT. We tracked the evolution of the source on the hardness-intensity diagram and find that the source oscillates between two main states: one characterised by a hard and luminous spectrum and the other at low hardness and luminosity. The properties of the soft component remain constant between the two states, suggesting that changes in the mass-transfer rate are not driving the spectral transitions. Instead, the bi-modal behaviour of the source and the known super-orbital period would point to the precession of the accretion disc. Here, we tested two theoretical models: (1) Lense-Thirring precession, which can explain the super-orbital period if the NS has a magnetic field $B$ $\lesssim10^{10}$ G, supporting the idea of M81 X-6 as a weakly magnetised NS, and (2) precession due to the torque of the NS magnetic field, which leads to $B \gtrsim$ 10$^{11}$ G. However, the latter scenario, assuming M81 X-6 shares similar properties with other NS-ULXs, is disfavoured because it would require magnetic field strengths ($B>10^{15}$ G) much higher than those known for other pulsating ULXs. We further show that the contribution from the hard component attributed to the putative accretion column sits just below the typical values found in pulsating ULXs, which, together with the low value of the pulsed fraction ($\leq10$\%) found for one XMM-Newton/pn observation, could explain the source's lack of pulsations. The spectral properties and variability of M81 X-6 can be accounted for if the accretor is a NS with a low magnetic field. Under the hypothesis of Lense-Thirring precession, we predict a spin period of the NS of a few seconds.