[Michael Cule]

I think that the question depends on things you would have to decide on the truth of in your particular Yrth.

The basic GURPS Magic system gives you a lot of tools that could be used to investigate the truths behind magic but no clear guidance about the implications of it.

I think what the attitude of the religious authorities would be towards Elementals would come from what the Thaumatological facts were and you have to think about that. (Well, except for the authorities in Al-Haz because they would be agin them and not interested in further investigations.)

Which comes down to: how are elementals summoned? Are they created or pre-existing? What happens to them after their bodies are destroyed? Are they people? Animals? What?

The rules seem to imply that they are created at the first point of their summoning and imbuded with what sentience they have by their first summoner. But that is rather disturbing. You are creating something with intelligence and awareness in the human range and giving it indefinite existence. This might be seen as usurping God's powers and function.

Do they have souls? (This can be determined using magic.) Are they automata or do they have something approaching free will?

How did the elves (who presumably taught the humans the spells to Create, Summon and Control Elementals) think of them? Do the human religious authorities believe the elves?

All has to be determined by the GM. Personally, since I have all the moral angst I need from magic with questions of when a foetus gets a soul, where they come from, whether damnation and salvation are real and other stuff, I tend towards:

They are magically created Automata.
They have no souls but do have low level minds without any initiative beyond what is needed to survive.