Rare earths are vital for military equipment. This action is coming from a country that NATO has trusted with its best technology and they continue to flirt with both Russia and China, NATO's primary threats.
No. The US kicked NATO member Türkiye out of the F-35 program and denied them F-16 upgrades for a long time[1]. And the EU has denied Türkiye membership supposedly because they're not fully part of Europe (among other issues) while courting Georgia which is farther east. Türkiye is treated as a frenemy by the west. Good on them for making their own way.
Those words are doing some heavy lifting. The EU cares more about their commitment to democracy, and their dubious economic policies. The last thing the EU needs is another Hungary.
My instinct is that there are a lot of a potentially good reasons not to let them into the EU, and maybe even ones for kicking them out of NATO, but "they want to sell their minerals to other countries" doesn't strike me as a reasonable gripe in terms of NATO at least.