It is really quite simple. In the case of GPS, those satellites will continue to orbit in the same path as before. The change in wobble of the Earth will place different soil beneath them relative to orbit time past the UTC line. This will require compensation to the tables in GPS receivers. The good news is that the satellites will send updated tables to everyone's tables.
In the case of navigation by sextant, the location of the sun and sighting stars will change with respect to location of the observer and time. This requires that the sextant user replace all of his printed charts. It will also affect the math required to apply the charts to the observer's position throughout advancing date and time.
Navigators are still taught to use the sextant since having GPS satellites is not really guaranteed in time of war.
Fair enough.