Is it possible to make a high-impedance voltage follower using a fully-differential op amp?
The input impedance of this circuit is equal to the input impedance of the op amp, which is normally very large.

It is even higher because of the following negative feedback (bootstrapping). It can be explained in such a way. The op-amp output voltage is equal and opposite to the input voltage (travelling the loop) and connected in series; so it is subtracted from the input voltage. As a result, the resulting voltage variations across the op-amp differential input are small. So the ratio dVin/Rin is small and the current variations are small. This means very high input differential resistance.

If I want an input impedance on the order of megaohms, is my only choice to put megaohm resistors in this circuit?

The professional solution is to put voltage followers (like the one in the first picture) or non-inverting amplifiers before the fully differential amplifiers. This topology is used in instrumentation amplifiers.
&quot;Putting megaohm resistors&quot; will cause undesired voltage drops across them and other problems.