How securely unguessable are GUIDs?

UUIDs/GUIDs are specified by RFC4122. Although Version 4 UUIDs are created from random numbers Section 6 makes an explicit statement on security:

Do not assume that UUIDs are hard to guess; they should not be used
as security capabilities (identifiers whose mere possession grants
access), for example. A predictable random number source will
exacerbate the situation.

A good discussion of the randomness of GUIDs can also be found in this question:

How Random is System.Guid.NewGuid()? (Take two)

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