Don't they have less to do with the EU than any other overseas territory of an EU member state?
They have common mackerel and herring quotas with EU and Norway, so you could surely find some islands somewhere that had less to do with the union.
Cooperation is based on a Fisheries Agreement from 1977 and a Free Trade Agreement from 1991. They are not in Schengen.
Fishing quotas is the major bone of contention and 2013-14 EU actually sanctioned the Faroes because they fished too many mackerells and herrings, so DK near the end of the conflict had to boycott a part of our state (which is ridiculous). Like not allowing Faroese ships to buy provisions in Danish harbours etc.
I meant in terms of their official relationship to the EU; as DavidB. said, they're not "Overseas Countries and Territories" like Anguilla, Aruba, New Caledonia, Greenland, etc.
But apparently, per Wikipedia, Akrotiri and Dhekelia, the Channel Islands, the Isle of Man, and Northern Cyprus are in the same boat as the Faroes.
