You should beware that the term "grand unified theory" (GUT), even if it sounds very general, has a very specific meaning in theoretical high energy physics: it refers very specifically to models that replace the gauge group of the standard model of particle physics by one big simple Lie group (in the technical sense of "simple"). For an excellent technical but expositional discussion of what GUTs really are see Baez-Huerta 09. For an excellent account of why physicists think this is a good idea see Witten 02. I expect that if you read that article (which is notes from a public talk, so should be readable for laymen, to some extent) to the end, you will at least feel an inkling of what makes GUTs fascinating intellectually, and it is not related to any theism.

On the other hand, what I guess you are really thinking of in your message are not so much GUTs in the sense as used in theoretical physics, but rather are what physicists call theories of everything (TOEs). That terminology, too, is usually used in physics with more specific meaning than its natural language meaning would suggest, namely it refers foremost to unifications of the standard model of particle physics with quantum gravity, but it is used more generally than the term "GUT", at least, by physicists.

Most people would think that it is quite obvious why intellectually one is tempted to look for a TOE: given two different theories of nature, the standard model of particle physics on the one hand and Einstein gravity on the other, which describe different aspects of fundamental nature, it seems more natural to wonder how they might be two aspects of one single theory than to be content with having two incompatible theories of fundamental nature.

Therefore on a superficial level I would tend to outright reject the suggestion that questions of theism have the first bit to do with the search for ever more fundamental theories of physics.

On the other hand, on a more subtle level I could agree that there is some relation, but I am not sure if we'd meet on that level. But let's see.

So one thing that is curious about the idea that there could be a TOE is that, at least the way it is usually imagined, it would, by definition of its common meaning, be a piece of theoretical physics hence of mathematics, really, which "in principle" encodes all of tangible reality.

When taken fully seriously, such a state of affairs would be a realization of a strong form of idealism, namely it would mean that "the world" in the end is pure thought, to the extent that it is embodied in a physical theory, which after all is, one imagines, a bunch of mathematical axioms and deduction rules.

The existence of a TOE would hence realize a form of idealism as the statement that the world is intelligible, and intelligible to the very end.

Such a strong form of idealism might remind one of Hegel's system -- as it did remind David Hilbert in a famous public lecture a century ago, who there ponderns theories of everything as Weltgesetze and reflects on whether it might indeed be possible to derive the whole world from pure thought (he ends up being scared away from this though, see the pointers here) . Now in Hegel's system, of course, all is unified, the physical laws of nature, the monotheistic god, the spirit, the spirits, the ideas, the whatnot. If you'd argue that physicist's hope in the existence of a TOE is closely related to a theism as in Hegel's system, than I would actually be inclined to follow you, but probably you don't (?)

What is curious in this respect is that theoretical physicists these days, the more fond they are of the idea of reducing all of reality to physical theory, hence to pure thought, the more dismissive they tend to be of philosophy (links). That's ironic and, I think, a sign of intellectual weakness that in the face of what is looking like a grand unification of physics with (idealistic) philosophy, neither camp recognizes the other. But apparently the world spirit has to still work on this... ;-)