You don't use a GNSS for nukes or ICBMs, because you assume in the former case that you are operating in a "RF contested environment" (i.e. a honking great EMP burst has hosed your radios) and in the latter case because most of the key exo-atmospheric maneuvering happens in an environment where line-of-site of stars is guaranteed (i.e. space).
But your point is valid: the reasons to limit access for security reasons are gibberish, because while not all EU nations are NATO members, a whole lot of them are. Gallileo will make the EU less vulnerable to peculiar US interference, so an argument that the UK shouldn't be able to CONTROL the constellation is sound, but the argument that they shouldn't be able to use it is not.