Let's say China decides to go ahead and block shipments of rare earth materials to Western countries. Is there a way for NATO members to retaliate and block crucial shipments to China?
There is a common misunderstanding about rare earths: They are not rare at all. The problem is that producing them is very, very damaging for the environment. Since that damage is only a cost for the producer if the producer's government says so, China can undercut any US producer.
But if China stopped selling rare earths, the USA (and many other countries) could easily produce them, if they are willing to accept that the environmental damage will happen in their own country and not in China.
Isn't the US doing that already by imposing restrictions on technology exports to China, e.g. recently on Huawei, in what some have described as a "tech cold war"? In general, the extractive industry has taken a back seat in developed countries. So NATO countries don't have to respond with symmetrical restrictions on raw materials.
In more detail as to one of the implications:
Barely 24 hours after news broke that Google revoked Huawei’s Android license, plunging the tech sphere into chaos, the U.S. Commerce Department told Reuters that Huawei will be granted a “temporary general license.” This license, which lasts until August 19th, allows Huawei to “maintain existing networks and provide software updates to existing Huawei handsets.” The license does not allow U.S. companies to work with Huawei on new products, however. [...] The company [Google] will now send software updates to Huawei phones until August 19th.
There are also several other restriction, relating to chips with US IP that Huawei uses from Qualcomm, Intel, Xilinx, or Broadcom. It's not clear if these chipmakers have been given any exemption and they all announced suspending cooperation with Huawei.
Also, I think that the assumption that the rest of NATO is willing to follow the US on this is rather tenuous given that even CoCom was a lot less enthusiastic in following the breadth and depth of US sanctions/restrictions on the Soviet bloc.
In 1991, the Survey of US Export Control Compliance Costs estimated that the United States had lost $9-10 billion in overseas sales each year due to communist export controls. As a further consideration, the “disincentives” inherent in the export control system caused American businesses to forego an additional $30 billion in sales to Russia, Eastern Europe and China alone. In contrast, West German machine tools sales to Russia in 1989 stood at $500 million with Japan at $200 million compared to the United States with a mere $1.5 million. While the American business community continued to lodge frequent complaints and warnings on the arbitrary and ineffective nature of containment trade strategies and bans, little was done to alleviate excessive US controls until the entrance of the Clinton Administration, along with the end of COCOM, in the mid and late 1990s.
Prior to the Trump administration, the US, EU and Japan had a more or less a common approach to Chinese export restrictions, (successfully) challenging them at the WTO.
However (breaking news) in the case of IP the unilateral US sanctions/restrictions may be surprisingly powerful, because of all the cross-licensing (particularly of patents) that goes on within the high-tech industry this days. Case in point, ARM (a UK-based and Japanese-owned company) announced breaking off relations with Huawei as well because its IP contains (some) "US origin technology":
ARM instructed employees to halt "all active contracts, support entitlements, and any pending engagements” with Huawei and its subsidiaries to comply with a recent US trade clampdown.
ARM's designs form the basis of most mobile device processors worldwide.
In a company memo, it said its designs contained “US origin technology”.
As a consequence, it believes it is affected by the Trump administration's ban.
One analyst described the move, if it became long-term, as an “insurmountable” blow to Huawei’s business.
He said it would greatly affect the firm's ability to develop its own chips, many of which are currently built with ARM’s underlying technology, for which it pays a licence.