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A couple of dozen Earth-like planets orbiting M dwarfs have been discoveredso far. Some of them have attracted interest because of their potentiallong-term habitability; such a possibility is currently vigorously debated inthe literature. I show that post-Keplerian (pK) orbit precessions may impactthe habitability of a fictitious telluric planet orbiting an oblate late-type Mdwarf of spectral class M9V with $M_\star=0.08\,M_\odot$ at$a=0.02\,\mathrm{au}$, corresponding to an orbital period $P_\mathrm{b}\simeq4\,\mathrm{d}$, inducing long-term variations of the planetary obliquity$\varepsilon$ which, under certain circumstances, may not be deemed asnegligible from the point of view of life's sustainability. I resume theanalytical orbit-averaged equations of the pK precessions, both classical andgeneral relativistic, of the unit vectors$\boldsymbol{\hat{S}},\,\boldsymbol{\hat{h}}$ of both the planet's spin andorbital angular momenta $\boldsymbol S,\,\boldsymbol{L}$ entering$\varepsilon$, and numerically integrate them by producing time series of thepK changes $\Delta\varepsilon(t)$ of the obliquity. For rapidly rotating Mdwarfs with rotational periods of the order of $P_\star \simeq0.1-1\,\mathrm{d}$, the planet's obliquity $\varepsilon$ can undergo classicalpK large variations $\Delta\varepsilon(t)$ up to tens of degrees overtimescales $\Delta t \simeq 20-200\,\mathrm{kyr}$, depending on the mutualorientations of the star's spin ${\boldsymbol J}_\star$, of $\boldsymbol S$,and of $\boldsymbol L$. Instead, $\Delta\varepsilon(t)$ are $\lesssim1-1.5^\circ$ for the planet b of the Teegarden's Star. In certaincircumstances, the M dwarf's oblateness $J_2^\star$ should be considered as oneof the key dynamical features to be taken into account in compiling budgets ofthe long-term habitability of rocky planets around fast spinning late M dwarfs.(Abridged)

Post-Keplerian obliquity variations and the habitability of rocky planets orbiting fast spinning, oblate late M dwarfs