The name is somewhat confusing. Rare earths aren't particularly rare. They're about a hundred thousand times more common than actually rare metals like platinum and gold, and about a hundred thousand times less common than common metals like iron, magnesium, and sodium: https://en.wikipedia.org/wiki/Abundance_of_elements_in_Earth...
Some of the metals mentioned in the article, like cobalt, ar neither rare nor rare-earth. Others, like indium and gallium, are about as rare and as expensive as silver, but are used in much smaller quantities.
Yes, rare elements help a lot with efficient wind turbines and CIGS thin-film solar cells (although note that CIGS contains rare metals, but no rare earths). But they aren't used at all in the silicon photovoltaic cells that dominate the solar market now and for the foreseeable future, which don't use any rare minerals at all. And you can build efficient wind turbines without rare earths if you have to; you just use field coils instead of rare-earth permanent magnets. (In fact, Abraham reports that GE wind turbines have already made this switch.)
In direct contradiction to what Abraham says, nearly all chips are 100% rare-earth free and rare-metal free, except for gold, which is in no danger of supply shortages. A small fraction of high-speed bipolar chips use gallium arsenide, which depends on rare gallium, but they're almost entirely limited to microwave-and-up RF analog circuitry these days.
And, of course, rare metals are 100% recyclable. They aren't a resource we can use up, except by launching them on space probes or burning them in nuclear reactors. If we're allocating them inefficiently, we can melt down our existing air conditioners and wind turbines to redeploy our neodymium to higher-priority uses. It won't be long before people are digging LCD panels out of garbage dumps to recover the thin-film indium: maybe five to thirty years.
This is a big issue if you're in the business of making motors, generators, or LCD panels. It affects your material costs significantly, and indeed indium cost volatility has been a major problem over the last decade or two. But it's not an issue at the level of human society as a whole.
I think the overwrought rhetoric here is deeply harmful because we really are facing real resource shortages: oil (though not this year), ocean-water buffers, and our atmospheric capacity to handle carbon dioxide. Hyping up bogus "resource shortage" dangers like this will just lead to the public dismissing the real dangers.