If that's true - then any map with curved lines of longitude cannot be correct...period.
That means that the map on the right CANNOT be correct.
How do you know whether the longitude line you are currently at is pointing North?
Obviously, lines of latitude and longitude are imaginary map-makers's things. We normally define them by reference to true north, east and west...relating to the axis of rotation of the Earth. A degree of latitude or longitude is measured relative to the center of the Earth.
So in FET, the concept is pretty meaningless. However, what we're talking about here is where the compass points relative to where the pole star (or southern cross method) shows us the poles.
In RET, the magnetic poles wander around a bit over time - but there is (at any given time) a definite position towards which all compasses everywhere in the world point. The motion of the magnetic poles has been known (and tracked) since around the 1600's - and navigational charts for airplanes and ships are always careful to explain this.
In FET, using the map on the right of the image above is that EITHER the light from Polaris and the Southern Cross stars has to curve (Tom says light doesn't do that) OR the compass has to point toward different places depending on where you are on the surface. That doesn't match what sailors (and subsequently airmen) have known for hundreds of years.
In FET using the map on the left, produces the expected results in the Northern Hemisphere - but do something crazy in the South. Beyond the equator - in the southern hemiplane - a compass still points North - but the Southern cross would have to be simultaneously in wildly different places for different viewers in order for it to match what real sailors and airmen see.
If FET is true then the compass needle would have to 'flip' from pointing with "North" towards the Northern (magnetic) Pole to pointing with "South" towards the southern magnetic pole as you crossed the equator. That doesn't happen - but it must if the compass heading is to be consistent with the direction from celestial navigation.
Neither map works...they are both equally "broken".
Tom may yet tell us that there is some other (as yet unknown) map that will resolve this - but it can't. You can't simultaneously have the needle point to the magnetic north and toward the magnetic south as it does in reality...and ALSO have it point (with an appropriate error) toward Polaris and the Southern Cross.