To what degree can the Rare Earth Elements be interchanged in its workaday applications?

In their humdrum pedestrian "high-tech applications due to their unique magnetic properties", how interchangeable are the Rare-Earth Elements (REEs) if, e.g., the US lacks one of them?

Rare earths are not rare, but they're chemically very similar. (This is because when you go to higher atomic numbers, they start filling the $$\mathrm{f}$$-shell, but the $$\mathrm{f}$$-shell is lower in energy than the $$\mathrm{d}$$-shell, so it's "hidden" by the $$\mathrm{d}$$-shell. The $$\mathrm{d}$$-shell is the valence shell and is the same in all of them, so their chemistry is almost the same.)

Separating two chemically similar substances is expensive. Separating 15 of them is much worse. This means that the mining part is easy, but the processing plant on the site costs about \$500 million. This is why rare earth mines are so few in number.

Another expense involved in lanthanide production is separation and disposal of the radioactive isotopes from the ore. At one time, for example, gas lantern mantles contained mildly radioactive $$\ce{ThO2}$$, but those are no longer available in many countries due to concern about the alpha emitting thorium and the alpha and beta emissions from daughters.