Rare earth metals are used for things like specialty alloys, which are used for all sorts of things, both military and otherwise. You can't just "find alternatives" for those -- instead, you need to find a different source, or come up with different alloys (a much more difficult task).
FWIW, Africa used to be the main source for those metals, along with Russia. So China isn't really the only source -- they're just the ones who currently have market share.
Still, they've created a kind of an environmental mess so they are really cutting back for the next decade or so while they clean up their mines, extraction processes, and mine tailings.
It all makes sense ~ even the Chinese have problems with radioactivity.