  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.
