The (magnetic) poles can shift all they want but the Equator will not change at all. You would have to change the axis of the Earth’s rotation to do that. Do that, and the Space Elevator is the least of your problems.
There has been evidence found of physical equator shift in the earths history. There have been theories that when the earths magnetic poles flipped (not shifted) that the earth “tumbled” until it regained equilibrium. Regardless, as you said, if that happened the space elevator would be the least of our problems.