OK, I obviously didn't explain myself very well, so I will try again. Please bear with me since these are new ideas to me, though I am sure they are not new ideas in any sense.
I am arguing by means of definitions. That is why I invoked the idea of logical impossibility, though even there I am not completely sure since I haven't thought this through completely.
What do we mean by material? In the past this was easy since it meant "made of matter". But now the line between matter and energy has been irrevocably smeared. They are equivalent.
We used to use the idea of spooky action at a distance as the analogy of the immaterial affecting the material world. Now we know that gravity, the biggest spooky 'actor' at a distance in the book is a routine material force at home in the materialistic universe. 'Energy' played a similar role -- just look at those metal filings lining up. We now speak of four forces, three of which we have 'explained' or at least cobbled together in a unified theory and they act via 'particles'. This 'stuff' that is not made of matter supposedly but acts on matter was always our analogy for the immaterial acting on the material world. But now we know that it is all material.
So, we turn to consciousness. Thoughts. They are immaterial, right? The only experience we have of thoughts is our own and those we discuss them with. I cannot point to a thought and say -- look, there it goes. Thoughts have existence only in their instantiation within our brains -- that is how they can have an effect in the material world/plane.
These are, of course, our experiences and refer to the material world, and you may argue that it is unfair to discuss the immaterial by recourse to the material.
But what do we mean by 'immaterial'? It is defined in contradistinction to 'material'. I have no means of discussing the immaterial except by recourse to the material because that is how immaterial is defined.
What do we mean by 'material'? In essence, it means that which has an effect within the world. If something takes up no space, cannot be detected, has no force in the world, then it is not part of the material world. It is immaterial, the opposite of material.
While we used to speak of immaterial forces in the world -- gravity, light, etc. -- we now know that they are material. We know they are material because they act in the world. We can measure them, quantify them, etc.
The immaterial, by definition, is not material. One of its properties, if we can even speak of such a thing should be that it has no effect on the world. If it did have an effect on the world then we would call it a material force. It might be one that we do not currently understand, but if those things that have an effect in the material world are defined as material (that is how we use the word now that we understand the equivalence of matter and energy, energy being a measure of things that have an effect in the material world), then the immaterial, by definition, cannot affect the material world.
So, to answer your questions: God moving the moon with his mind would constitute a new material force that can be measured. It wouldn't be immaterial. God's mind would therefore be material.
Second issue, a mind that is 'immaterial' doesn't make sense. It has no boundary. I don't see how you could define such a 'thing'. Mind is only sensical as a term if it has a boundary. Thought can only occur by contrast, comparison, analogy, etc. which require boundaries. I could try and fudge a concept of an 'immaterial mind', but I would only be fooling myself. I see other people and they seem to think. I cannot see their minds, so I think mind is immaterial. But that is because mind is not a 'thing', it is action. Action requires something that acts. The immaterial acting makes no sense. By definition there isn't anything there to act in the first place.
What is my problem with magic? It is cheating. It destroys any possibility of rational discussion. My magic can make a square circle. If 'magic' can be invoked to perform logical impossibilities, then there is no sense in discussing any of this once it is brought into the picture.