Well, it is probably not any sort of problem for us if the water we pumped out of aquifers does slightly alter the rate of precession of our rotational axis, or even the location of the magnetic north pole. The problem is that we are going to run out of groundwater to pump in several areas where that has become an important part of agricultural production.
That said, I am willing to believe that the amount of standing water reduction in aquifers, along with the loss of glaciers and mass in polar ice caps, can make miniscule changes in the rate of precession of our rotational axis. I have long suspected that the build-up and melting of the huge ice sheets, mainly in the northern hemisphere, probably altered the precession rate much more significantly, since the water came mainly from equatorial ocean areas (about 325 feet of depth) and piled up on northern temperate and arctic areas (to depths of 1-to-2 miles). That should affect the rate of precession and even the length of the day, as mass is moved to different radii of rotation.
This effect might be needed in the climate models to get their ice age periods to more accurately line-up with the Milankovitch Cycles, since it actually changes the periods of some of those cycles.
But, it is not a simple calculation as if the Earth is a ridged rock. We know that the ice sheets cause the shape of the rock/soil surface of the Earth to change, getting closer to the center under the ice and bulging up elsewhere. So, that partially compensates for the ice buildup. But, because the melting was so fast from about 25,000 years ago to about 15,000 years ago, the Earth's shape has not changed back to its ice-sheet-free shape, yet. Where I live now, the land surface is still sinking about 1 foot per century.
So, while not a reason to panic, the results of the study are still interesting with respect to learning about climate effects over long periods.