Insulated GEC (Grounding Electrode Conductor)

If the copper wire is electrically connecting together other conductors (buried plates, driven rods, etc.) that make contact with the soil then I can see this buried conductor could be insulated. It makes no sense to me to use insulated wires in the ground to make an earth connection.

Earthing connections can be the most baffling thing in an electrical installation. They change wildly depending on local regional conditions. Get an authorized copy of the standards approved for earth connection for this location and present them to your customer. If you find that none exists, contact a local electrical firm and pay them for their opinion of standard practices in the area. I suspect your customer is misreading a document or a poor translation of the document. Without having any document to present, you have nothing to stand on.

Quite normal under BS7671

Look at:
542-3
542-3-2
543-2
Table 54.1

You also need to look at BS7454

Perfectly normal. It violates no standard or code. What are the soil/sand conditions? Acidic! So the conductor is insulated and the connections of the earth conductor should be wrapped with Denso tape to prevent further corrosion at the joints/cadwelds. Common practise in many countries.

Insulate the Ground Rings...or insulate the GEC's?

Insulating Ground Rings makes no sense. They are there to make contact with the earth.

Insulating/protecting the bonds from the soil conditions...fine.

Ground rings and Ufer earthing aren't commonly used under BS7671. A nest formed of deep driven rods connected by insulated/protected conductors being preferred.
Due to me working mainly to the UK's M&Q (mines and quarries) regulations the above methods are used on new installations.

I was quite surprised to see in a document from one of our DNO's (district network operators) that an Ufer earth is now required for the MV switchrooms I'm building at the moment. I'd already planned to use both a ground ring and an Ufer earth.
This is the first time I've seen either of them as a requirement.

If the OP is required to work to BS7671 he should also get the following documents, EaWR and ESQCR.

This seems a bit over board for the UK. Normally Ufer earths are used in very dry ground conditions and the UK has extremely wet soils. I understand there is a cost saving to be gained as steel rods, encased in concrete can be used and the conductor can be reduced. Is there some other reason that this is now being implemented or is this just peculiar to the site you are working on?

Quarries tend to be a bit deficient on the topsoil side of things so some method has to be used. The earlier plants used deep rods in boreholes back filled with Bentonite. The water table is often low which doesn't help.

Why UKPN now want an Ufer earth I don't know, I've never seen it specified before.

As you know this could be changed for almost any good or silly reason.